HP 20B User Manual

HP 20b Busine ss Consultant Financial Calcul ator Manual For free tra ining, visit w ww.hp.com/go/ca lctraining HP part num ber: F2219-90 201 First edition: August 2008
Le ga l N ot i c es 2 Legal Notices This manual and any exam ples contai ned herein are provid ed “as is” and are subject to change with out notice. Hewlett-Packard Company makes no warranty of any kind with regard to thi s manual, including, but not limited to, the implied warran ties of merchantability, no n-infringement and fi tness for a particular purpo se. Hewlett-Packard Co mpany shall not be liable for any errors or for incidental or c onsequential damages in c onnection with the furnishing, perf ormance, or use of this manual or the examples c ontained herein. Copyright © 2 008 Hewlett-Packard Development Compa ny, L.P. Reproduction, a daptation, or tran slation of this manual is prohibited wi thout prior written permission o f Hewlett-Packard Company, excep t as allowed under the co pyright laws. Hewlett-Packard Co mpany 16399 West Bernardo D rive MS 8-600 San Diego, CA 92127-1899 USA Revision History Revision Hist ory Revision Date Edition 1, v. 12 August 7, 2008
Contents 3 Contents Legal Notice s Revision History ............................................. .................................................................... . 2 HP 20b Business Consu ltant Keyboard Keyboard Map Legend .................................. ............................................................... ...... 6 1 Basic Features Welcome to the H P 20b Fin ancial C alculator .......................................................... ........... 7 Turning the Calculator On and Off ............................................................... ....................... 7 Selecting a L anguage ..................................................... .................................................... 7 Adjusting the Display C ontrast ........................................ .................................................... 7 Cursor ..................................................... .................................................................... ........ 7 Two Line Display ......................................... ............................................................ ........... 8 The Mode Menu: Setting Preferen ces ......... ............................................................ ........... 8 Changing the Calculation Mode ...................................... .................................................. 10 Key Presses an d th e Se condary Function : Ke y .................. ........................................ 11 Annunciators .................................................. ............................................................... .... 11 The I Key ............................................. ............................................................ ......... 12 The = Key . .................................................. ............................................................... .... 12 Using the I and = Keys .................................................... ...................................... 12 Editing and C learing Entries ....................................................... ...................................... 13 The On/CE O Key ..................................................................................... ..................... 13 The Reset :x Menu .................................................. .................................................. 13 Notes about Special Menus ...................................................... ........................................ 13 Memory and the Memory Menu .................................................. ...................................... 13 Accessing Menus an d Menu Maps ............................................................ ....................... 14 2 Mathematical Ca lculations Mathematical Functions ...................................... .............................................................. 16 Number Entry and Display ................................................... ............................................. 16 Chain Mode ....................................... ............................................................... ................ 17 Algebraic Mode ........................................................ ......................................................... 17 Reverse Polish Notation (RPN ) Mode .. ....................................................... ..................... 18 The RPN Stack .......................................................... ....................................................... 1 8 Last Number ....... ............................................................ .................................................. 19 One-Numbe r Functions and the Math Menu ....................... ............................................. 22 The Math :s Menu . .................................................. .................................................. 23 The Probability Sub-menu .............................................. .................................................. 25
Contents 4 Two-Number Functions ................ ............................................................... ..................... 26 Storing a nd R ecalling N umbers ................................................ ........................................ 27 Recall Arithmetic ............................................ ................................................................... 28 Storing a nd R ecalling w ith Time Value of Mone y ( TVM) Keys ... ...................................... 28 Recalling a M enu I tem Value in a Me nu ....................................................................... .... 28 Rounding Numbers ............................................. .............................................................. 28 Percentages ............................................ ................................................................. ......... 28 3 Time Value of Money Time Value of Mone y ( TVM) Keys ............................................................. ....................... 30 Calculating Payments on a L oan .............................. .................................................. 32 Amortization ................................................. ............................................................ ......... 33 Creating an Amortization Schedule ..................................................... ....................... 34 Interest Conversion Menu ................................... .............................................................. 35 Using the I nterest Conversion Menu ........ ................................................................... 35 Canadian Mortgage s: TVM Ca nada ..................................................... ............................ 36 Canadian Mortgage Example .................................................... ................................. 38 4 Cash Flows Cash Flow Example ................................................... ....................................................... 4 0 Analyzing C ash Flo ws ............. .................................................................... ................ 42 Editing Ca sh F lows .................................. ............................................................... .... 44 Sample C ash Flow Diagrams ................................................... ........................................ 45 5 Bonds The Bond Men u ........... .................................................................... ................................. 46 Bond C alculation E xample ..................... ................................................................. .... 47 6 Date C alculation The Date Calculation Me nu ... ............................................................... ............................ 49 Date Calculation Example .......... ............................................................ ..................... 49 7 Break-even The Break-even Menu . ............................................................... ...................................... 51 Break-even Example ... .................................................................... ............................ 51 8 Business Problem s The Percent C alculation Menu ........................... .............................................................. 53 Percent C alculation Examples ............................................................. ....................... 54 9 Depreciation The Depreciation Menu ............................... ............................................................ ......... 56 Depreciation Example ............. ............................................................... ..................... 58 10 Statistical Operat ions The Data and Stats Me nus .............................................................. ................................. 61
C on t en t s 5 Statistics Example ....... .................................................................... ............................ 63 11 Errors Error Messages and Calculator Status ... .................................................................... ...... 65 12 Warranty, Regulat ory, and Contact Informat ion Replacing t he Batteries .............................................. ....................................................... 6 7 HP Limited H ardware Warranty and Customer C are....................... ................................. 67 Customer Care ............................. ............................................................... ..................... 68 Product Regulatory & Environme nt Infor mation . .......................................................... .... 71 Index
H P 2 0b B us in es s C on s u lt an t K ey b oa r d 6 HP 20b Busine ss Consultant Keyboard Keyboard Map Legend No. Feature Chapter(s) No. Feature Chapter(s) 1 Time Value of Money keys 3 16 Annunciator disp lay area 1 2 Cash Flows, I RR, and NPV menus 4 15 Amortization and Depreciation menus 3,8 3 Data and Statistics menus 9 14 % key and Percent Calculation menu 2,6 4 Input key 1 13 Store and Recall 2 5 Memory menu 1 12 Break-even menu 6 6 Up/Insert and Down/Delete keys 1 11 Backspace key and Reset menu 1 7 Secondary function k ey 1 10 Math Menu 2 8 On/Off and cle ar entry key 1 9 Mathematical f unction keys 2
B as ic F e at ur es 7 1 Basic Features Welcome to the HP 20b Financial Calculator This manual is designed t o familiarize you with the ma ny f eatures of your new 20b Finan cial C alculator. It includes m enu maps, examp le problems an d solution s w ith key pre sses, screen shots, and example s o f cash f low diagram s. There are also sections whi ch list the er ror me ssages and explain how R PN works. Refer to the section t itled, Contents for quic k access to various topi cs. If you ne ed more information abo ut your calcu lator, or a bout calcul ator operation and features , please ref er to the training m aterials a vailable at: w ww.hp.com/go/ca lctraining. Turning the Calculator On and Of f To turn on your calcul ator, press O. To turn it off, press :a. Turning the c alculator off does not erase any data. The c alculator auto matically t urns itself off after approx imately five minutes to conserve e nergy. If you see the low ba ttery symbol ( ) in the display, r eplace the b atteries. See Chapter 12 , Warranty, Regulatory, and Cont act Informat ion for instructio ns on repla cing the batt eries. Selecting a Language English i s th e default language f or messages disp layed on the screen. To select a language other than English: 1. Press :u to acces s the M ode menu. FIX displays on the top line of th e screen. 2. Press < r epeatedly until English displays on the screen. 3. Press I until the desire d language is displayed . The display ed language is the acti ve setting. 4. Press O t o return to the default calculator screen. For more inf ormation on accessing menu s and changing calculator settings, r efer to the section s be low titled , The Mode Menu: S etting Pref erences , and Accessing Menus and Menu Maps . Adjusting the Display Contrast To adjust the contrast of the display, press and hold O while pres sing the or - keys. Each press of the or - keys slightly increase s or decrea ses the contra st of the d isplay. Cursor When you ent er a n umber, the cursor (_) b links in t he display and indicate s you ar e in number e ntry mode.
Basic Features 8 Two Line Display There are two lines in the dis play screen as shown in Figure 1. Figure 1 Dis play Screen The top line of the screen d isplays operation status, op erator symbols , annunciator s, an d abbrevi ations of the registers, variables, and menu na mes. Throughout this manual, this lin e is referr ed to as the top l ine . In Figure 1, SIN is on t he top line. The bottom l ine display s nu mbers you have enter ed, or resu lts. Throughout t his m anual, this line is ref erred to as the bottom line . When no operations hav e been entered and n o operations are pending, the bottom line of t he screen displays 0.00 . T his state of the c alculator is referred to as the default calculator screen . The Mode Menu: Setting Pref erences The Mode m enu allows y ou to customize t he calculator . To acces s t he Mode menu, pre ss :u. Press < or > repeatedly to scroll throu gh the men u starting with FIX=2 (the numb er of digits displayed to the right of the decimal point). Once an item is display ed, press I to cycle t hrough the other options for that setting. To exit the Mode menu, press O . Table 1-1 lists the items in the Mode menu .
Basic Features 9 Table 1- 1 Mode Menu Sett ings Setting (to p line) Description FIX= 2 Display prec ision (number of digits displayed to the right of the decimal point). Default is 2 . Key in the numbe r of digits you want and press I , or p ress = un til the n umber of digits you want is d isplayed. The d isplay precision can be any number from 0-11. If you specify -1, the calculator displays numbers with the most appropriate number of digits a fter the decimal point. If y ou find you need to ch ange the FIX setting often, use the following shortcut: 1 Press : and release it. Check that the secondary function indicat or is displayed. 2 Press : again, and, without r eleasing it, press a key, 0 through 9 that corresponds to the desired FIX setting. FIX se ttings for 10 and 11 are not available using this shortcut. If you press . instead of a nu mbered key, FIX=-1 is selected. Degree or Radian Angular mode in degrees or radians for trigonometric functions. Default is Degree . Pressing I t oggles between these options. Date: mm.ddyyyy or dd.mmyyyy Format f or dates. December 3, 2010 is entered as 12.032010 in mm.ddyyyy format, or 3.122010 in dd.mmyyyy format. Note the (.) in bo th formats s eparating the first and second groups. Default is mm.ddyyyy format. Pressing I t oggles between these options. Note that when a date is dis played, a number between 1 and 7 also displays a t the right of the screen. This number indicates t he day of the week corresponding to that date. Mo nday is 1 , and Sunday is 7 . Note: in 360-day calendar mode (Cal.360), days of the week are displayed only if the da te is valid. 1.23 or 1,23 Selects point or comm a as decimal s eparator. Default is decimal point, 1.23 Pressing I t oggles between these options. 1000.00, 1,000.00 , 1000,00 o r 1.000,00 Selects thousands separator. Default is none, 1000.00 Pressing I t oggles between these options. Note: the 1000.00 a nd 1,000.00 options are only ava ilable if the decimal separator is set for p oint (.) ; 1000,00 and 1. 000,00 are available on ly if the decimal separator is set fo r comma ( ,) . Chain, Algebraic , or RPN Calculation mo de. For m ore information, refe r to Chapter 2, Mathematical Calculations . Pressing I cycles through these options.
Basic Features 10 Table 1- 1 Mode Menu Sett ings Setting (to p line) Description English, Fra nçais, Deutch, o r Español Language s etting for the messages displayed on the scre en. Default is English . Pressing I cycles through these options. Actual o r Cal.360 Calendar options for b onds and date c alculations. Default is Actual . Pressing I t oggles between these options. Annual or Semiannual Bond type. Default is Annual . Pressing I t oggles between these options. TVM St andard or TVM Canada Activate o r deactivate the compounding pe r year (C/YR) op tion in time v alue of m oney (TVM) calculations. T his option is primarily used f or Canadian m ortgage calculations. F or more information, refer to the section titled, Canadian Mo rtgages: TVM Canada in Chapter 3. Pressing I t oggles between these options. Changing the Calculation Mode After viewing the default settings, suppose you want to change the c alculation mo de from Ch ain to RPN. See Ta ble 1-2. Table 1- 2 Changing the Calculation Mode Keys Display Description :u Opens the Mode menu, starting with first setting option, FIX , the number o f digits dis played to th e right of t he decimal point. <<<< < (Press five times) Scrolls to the cu rrent setting for t he calculation mode , Chain . II (Press two times) Selects RPN as the act ive setting. Note the sma ll RPN annunciator to the right. O Exits t he Mode men u and returns you to t he default calculator sc reen.
Basic Features 11 Key Presses and the Secondary Function : Key To execute t he function associated w ith a k ey, press a nd release t he desired k ey. Most of the 20b's keys have two f unctions: the primary f unction a nd the s econdary fun ction. The primary function i s printed on the to p of the key. The secondary func tion is printed on the bevel of the key. See Figure 2. R Primary Function Secondary (shifted) Function Figure 2 Primary and Secondar y Ke y Functions To activate the secondar y function of a ke y, press and release : followed by the key with t he d esired sec ondary function printed on the bevel. U nlike the shift key o n a typewr iter or computer key board, it i s not nec essary to pre ss and ho ld : while pressing a nother key. When : is active, t he dow n arrow annunciator appears on screen, indicat ing that t he next key pressed w ill exec ute t he secondary functio n of t he key. T o cancel an accidental press of :, simply press : a second t ime. In this manua l, comma nds using the secondar y key functions are represe nted by the secondary function k ey symbol, :, followed by t he key with the se condary funct ion. For ex ample, to e xecute sine , press :p. Note how th e SIN portion of the key i s highlighted, while the 7 is grayed o ut. Thi s highlighting f ocuses on the fu nction of t he key t hat w ill be a ctivated in a given command, and it is used thr oughout t he manual to make the examples easier to foll ow. Key commands for example problems are provided t hroughout the t ext and in tables. K ey symbols are placed i n the order they are to be p ressed, from left to right. Annunciators Annunciators are symbols t hat appear in the disp lay as m essages, or af ter certain keys or k ey comb inations have been pressed. Annu nciators are special sym bols indicating a specific st atus in t he calculator. Figure 3 i llustrates t he a nnunciator symbols in th e display.
Basic Features 12 Figure 3 Annunciator S ymbols in the Sc reen Display The I Key The I key is used t o input values for variables and exec ute menu it ems. The I key is also used in Reverse Polish Nota tion (RPN) mode to enter a number on the stack or dup licate it. The = Key The = key is use d at th e end of a mathemati cal operation to calculate t he final resu lt. For exam ple, 1 2= returns a f inal result of 3 . The = key, when pr essed outsid e of a m athematic al operation, a lso allows yo u to re quest a cal culation for the value of an item. This re quest only applies to items that can be calculated. Using the I and = Ke ys Suppose you w anted to calculate the effective interest r ate for a 12% nominal in terest rate w ith 12 p ayments per y ear in th e Interest Con version (IConv) menu. To open the IC onv menu, press :&. Nom %= displays on the top line, and the current value assigned to the nomina l interest rate is displayed on the b ottom lin e. With this screen disp layed, press 12I to input a new value for the nominal rat e. Press < f ollowed by = to calculate the value for the effective rate. See Figure 4. Figure 4
Basic Features 13 When an item for wh ich the = ke y is valid displays, the small an nunciator (=) is displayed o n the to p line at the right of the screen. Do no t confu se this small annunciator ( =) with the larger annu nciator (=) found to the r ight of a variab le. When an item for wh ich the I k ey is valid displays, t he I NPUT annunciator is displayed on t he top lin e at the right of the screen. Editing and Clearing Entries The On/CE O Key Pressing O one tim e cancels current number entries, mathema tical operation s, or a menu sele ction, in th at order. Pressing O repeatedly when perform ing multip le o perations can cels one oper ation at a time, f rom the la test to t he earliest. The Reset :x M enu The Reset me nu allow s you to reset some , or all, of the me nu items, v ariables, an d registers to their defa ult values. To open the Reset m enu, press :x. TVM displays on the top line. Press < or > rep eatedly to s croll to a specific item. To validate a choice a nd reset t he select ed items, pres s I. Press O t o cancel. If you s elect the command to r eset the cash flow ( Cash Flow ), stat istics ( Stats ), or a ll values ( All ) items, you w ill be prompt ed to co nfirm your choice. At t he Del. All? , Del. Data? , and Del. CF? prompts, press I again t o confirm th e reset, or O to can cel. While working within a sp ecific menu, pressing :x takes you directly to t he item of the Reset menu that allows you to reset that s pecific menu. For examp le, if you are worki ng in the Bond menu and you w ish to re set all yo ur entries in the Bond menu, with an y item of the Bon d menu displayed, pre ss :x. Bond displays on screen. At t his prompt, pressing I resets the Bond menu an d returns you to the last item you were w orking with in the B ond menu. Notes about Special Menus The Mode, Memory, M ath and Res et m enus ar e special m enus; if yo u were work ing in a menu pr ior to enteri ng one o f these special menu s, pressing O to exit them r eturns y ou to your previous m enu,. This feature al lows you to work in two or more menus simulta neously without having to exit a me nu. Memory and the Memory Menu The Memor y menu contain s the follow ing items: m emories 1-9 ( Mem 1-9 ) and 0 ( Mem 0 ), Cash Flow , St atistics ( Stats ), and Memory . To enter the m enu, press :t. Press < or > repeat edly to s croll through t he items starting wi th memory 1 ( Mem 1 ). When a memory item is displayed, you can e nter a new number and modif y t he value of the memory by pre ssing I.
Basic Features 14 For more inf ormation about storing and recalling n umbers, refer to the section titled, Storing and R ecalling Numbers in Chapter 2. The Cash Flow and St atistics me nus share t he same m emory and ar e limited to a comb ined total of 50 me mory slots. The number d isplayed with Memory refers to the num ber of rem aining memor y slots. When t he cash f low or stat istics items ar e displayed, a number also appears o n the bo ttom line. This number indicates the number of memory s lots used b y t he menu . Pressing I with this number d isplayed resets the memor y of the displayed me nu item an d erases all entered data. Since entering data in t hese me nus can repres ent a significant amount of work, you will be asked to confirm your choice. At the Del.Data ? or Del.CF? prompt s, pre ss I to conf irm, or O to canc el. Accessing Menus and Menu Maps Many of the calculator' s f unctions ar e located with in menu s. To acce ss a menu, press t he key, or secondary-f unction-key- combination, for the menu in wh ich you wi sh t o work. To exit a menu, pr ess O. For example, to access t he Break-e ven menu, press :!. On ce opened, y ou can scroll through the items in the menu by pressing <or > r epeatedly. W hen you arrive at the l ast item in a menu, pressing < re turns you to the f irst item. Similarly, pres sing > one time o n the f irst menu i tem scrolls t o the last item i n the menu . Most items consist of t wo parts: a name and an assoc iated number. For ex ample, the Fixed item in th e Break-even me nu (Figure 7) displays as s hown in Figure 5. Figure 5 The large ( =) annunciator shows that the val ue assigned to Fixed is 120,000 . If y ou perform a calculation with this item displayed by pressing 1 2= for example, Fixed is still selected as t he current item, but t he large ( =) annunciator is now turned off, indicating t he 3 is not t he value a ssigned to Fixed (see F igure 6). Figure 6 At this po int, to return t o the di splay of t he Fixed menu ite m shown i n Figure 5 , press O. Some menus h ave sub-m enus. If an item repre sents a sub-menu, pre ssing I with that menu item displaye d opens th e sub-menu.
Basic Features 15 In this manua l, diagram s called Menu Maps are include d at the beginning of each section t o assist you with n avigating through the m enus used f or that section. For an examp le of a menu map, see Figu re 7. Figure 7 The Menu Map for the Break-even Menu There are four types of menu it ems: 1. Read/writ e. Read/write m enu it ems, such as Fixed in the Break-even menu shown above, are easily recogni zable, because when they are s elected, both the INPUT and small (=) annu nciators are l it. When l it, these annun ciators indicate that en tering a number a nd pressing I will store the enter ed number in t he displa yed menu ite m. Pressing = (outside of a mathe matical operat ion) calcula tes the val ue for t hat item ba sed on ava ilable data. 2. Read-onl y. Read-onl y it ems such as Internal R ate of Return ( IRR% ) i n the IRR menu are display-only; the y are calculated values compute d internally by the calculato r. 3. Write-o nly. Write-only items, such as invest ment interest rat e ( Inv. I% ) in the Net Present Va lue (NPV) menu, are similar to read/write item s in that the INPUT annunciator is lit when t hese ite ms are s elected, indicat ing that e ntering a number and pressing I store s that n umber in that menu item . H owever, t he = key does not calculate a value for th at item. 4. Special i tems. Special items, such as the Degree/Radi an option in the Mode menu, th e items of the Reset menu, and the items of the Perc ent Calcula tion (�lc ) m enu perform a n action when I is pressed. De pending on t he menu, this a ction can be the selection of a sub-menu ( �lc menu) , changing a mode or setting (M ode men u), or erasing data (R eset men u).
M at he m at ic al C a lc u l at io ns 16 2 Mathematical Calculations Mathematical Functions Mathematical fun ctions are located:  On keys, such as, -*/ , etc.  On shifted, or secondary f unctions, such a s, : p  In the Ma th menu, :s Number Entry and Display Numbers are entered b y pr essing:  Numbered ke ys, 0 - 9  The decimal p oint .  The } key  The :w keys To correct a number entr y, press t he back space key, {. Each press of { er ases the la st digit or symbol y ou entered. To enter a number i n the d isplay, pres s the numb er digits su ccessively. A nu mber can have up t o 12 digits. To change th e sign of a nu mber from p ositive to negative, pres s } . Use scient ific n otation to enter ver y large and very sma ll numbers. For example, to enter the num ber 127 10 23 . 1  in scient ific notation, first enter the mantissa ( 1.23 ) and then press :w and enter th e number ( 127 ) representing t he e xponent. The exponent must have a value between -499 and 4 99. Figure 1 S cientific Notatio n in FIX= 2 Mode
Mathematical Calculations 17 Chain Mode Calculations in Chain m ode are interpreted in the order in w hich the y are entered . For example, ent ering the f ollowing numbers and operations a s written f rom left to right 1 2*3= r eturns 9 . See Figure 2. Figure 2 Calculation in C hain Mode Note: if yo u press an operat or key, -*/, after =, the calculation i s continued using the currently displayed va lue. In Chain mo de, if you wish to override the left to r ight order of e ntry, u se parenthese s () to prioritize operations. For example, to calculate   3 2 1   , you ma y e nter the problem as wr itten from left to right, with parentheses to prioritize the multiplication op eration. See Table 2-1 below. Table 2- 1 Simple Arithmetic Calculations in Chain Mode Keys Display Description 1 (2*3) Sets operat ional priority, inputs n umbers, and multiplies 2 an d 3. = Adds 1 to 6 a nd returns 7.00 on the b ottom line a s the final result. Algebraic Mode To set the calculator in Algebraic mode, refer to the section titled, The Mode M enu: S etting Preferen ces in Chapt er 1 . In Algebraic mode, mult iplication and d ivision have a higher pr iority than addition a nd subtraction. For exam ple, in Alg ebraic mode, pres sing 1 2*3= returns a result of 7.00 . In C hain mode, the same key presses return a res ult of 9.00. In Algebraic mode, operat ions between two numbers have the following pri ority:  Highest priority: the power function ( y x )  Second priority: combinations and perm utations  Third priority: multiplication and division  Lowest priority: addition an d subtraction
Mathematical Calculations 18 For example, key in 1 2 x 5 nPr2 2 in Algebrai c mode by pressing: 1 2*5: b2:m= . The resu lt is 241. Note: the ca lculator is limited to 12 pendin g operations. An operation i s pending when it is wait ing for the input of a number or the result of an operati on of higher pr iority. Reverse Polish Notation (RPN) Mode To set the calculator in RPN mode, refer to t he sect ion titled, The Mo de Menu: Setting Preferences in Chapt er 1 . In RP N mode, numb ers are en tered first, separated by pr essing I or =, follo wed by an o peration key. Note: press ing I or = is optional after entering a nu mber, if t he next key pressed is an o peration. Each time you press a n oper ation or fun ction key in RPN, the a nswer is calculated immediately and displayed. For example, suppose yo u wanted to add two n umbers in RPN, 1 a nd 2. Press 1I 2 . Th e result, 3.00 , is ca lculated and displa yed immediately on the b ottom line al ong with the ( ) symbo l on th e top line. Note: in RPN mode, w hen you ar e in a menu f or which I or = are valid, pressing t hese keys enters the number, but it als o performs the action as sociated with t he key for the menu item, w hich is generally saving t he number in the variable or calculating t he item's value. The RPN Stack RPN works b y placing numbers in storage register s called the stack . The RPN stack ha s four l evels numbere d 1-4. The levels are stacked o n top of one a nother. See Figure 3. Stack Level 4 Stack Level 1 Stack Level 3 -15 12 Stack Level 2 41 23 Figure 3 The RPN Stack In Figure 3, the stack contains fo ur number s, 2 3, 41, 1 2, and -15. Each lev el (1-4) conta ins one n umber. Whe n a numb er is typed and entered into the stack b y pressing I , this new number is " pushed" into level one of the stack, and each number a lready in the stack moves up one level. The number i n Level 4, -15 , is pushed out and is lost.
Mathematical Calculations 19 When an operation is perf ormed on the stack, addition ( ) for in stance, the c alculator "po ps" or moves the two numbers from the b ottom levels (Levels 1 and 2) out of the stack, perform s the operat ion, and " pushes" th e results back into the stack. With the n umbers entere d into the stack as shown in Figure 3, pr essing changes th e stack a s shown in Figure 4. Note that when the number s are "popped" out to a dd 23 a nd 41, Le vel 4 of the stack re mains unchange d. -15 -15 12 64 Figure 4 The RPN Stac k of Figure 3 after the Addition Operation Last Number Each t ime you perfor m a mathematical operation, the cont ent of Level 1 of the stack is saved. Pressing : d reca lls th at number. Th is f unctionality c an be u sed to undo an erron eous key pr ess, or if you w ant to reuse a number , such as 56.123 in the expres sion:     123 . 56 123 . 56 23 . 1  See Table 2-2 for an example using the last nu mber function. Table 2- 2 Last Number Keys Display Description :u3I Sets FIX= to 3.000 <<<<< II Selects RPN as the o perating mode. O1c23 I56c1 23 Inputs 1 .23 and 56.123
Mathematical Calculations 20 Table 2- 2 Last Number Keys Display Description :d/ Adds 1. 23 and 56 .123, then divides the sum b y the last n umber, 56.123. Returns results in t he selected display format. For more co mplex problem s requiri ng two or more oper ations, you do not need t o enter p arentheses to set o perational pri ority. Key in nu mbers and operations ins ide the parentheses first, followed by those outs ide of the p arentheses. If a probl em has more than one set of parenthese s, start by working wit h the op erations and n umbers in the innermost p arentheses an d work out. For example, calcu late:     6 5 4 3    One way t o calculate this pr oblem is to key in the numbers and operations within t he parentheses first, followed b y the operation outs ide of the p arentheses. See Ta ble 2-3. Table 2- 3 Simple Arithmetic Calculations in RPN Mode Keys Display Description RPN Stack 3I4 Inputs t he numbers and the operation in the first set of parentheses. I ntermediate results are displayed. Note the ( ) and (RPN) annunciators. Previous Valu e Previous Valu e Previous Valu e 7 5I6 Inputs t he numbers and the operation in the secon d set of parentheses. I ntermediate results are displayed. Note the ( ) annunciator.
Mathematical Calculations 21 Table 2- 3 Simple Arithmetic Calculations in RPN Mode Keys Display Description RPN Stack * Finishes t he operation and displays the results. Pressing I or = when you are not entering a number duplicat es the number on Le vel 1. That is, the number on Level 1 i s pushed on the st ack, m aking Le vels 1 and 2 equal. In the e xample above, pressing I after * duplicates 77 on the stack , ma king Levels 1 and 2 equal. S ee Figure 5. Previous Value Previous Value 77 77 Figure 5 Duplicating a Number on the St ack In RPN, th e parenthese s keys ( ) man ipulate the stac k. Pressing ( performs a roll d own of the stack. A roll down causes the stack to roll towards the bottom of the stac k, during wh ich the n umber in Le vel 2 moves down to Level 1, the number in Level 3 mo ves down t o Level 2, the number in Level 4 moves down to Level 3, a nd the number in Level 1 m oves up to Le vel 4. The ( ke y has a small down arrow on it as a reminder of the roll down feature. With th e numbers entered into the stac k shown in the left column in Figure 6, pr essing ( performs t he roll down of the stack shown i n the righ t column.
Mathematical Calculations 22 Figure 6 The RPN S tack and the Roll Down Op eration Pressing ) performs a swap . A swap operation exchanges the numbers on Levels 1 and 2 of the st ack. T he ) key has a small symb ol on it as a r eminder of the swap feature. With t he n umbers entered into the st ack shown in the left column in Figure 7, pres sing ) performs a swap to the stack a s shown i n the r ight column. Figure 7 The RPN S tack and the S wap Operation Note: when no menu is selected, t he < key pe rforms the same fun ction as th e ( key. Th e > key performs t he inverse operat ion called, rol l up . One-Number Functions and the Math Menu The key presses for th e one- number mathemat ical functions l isted in T able 2-4 be low apply to all mode s, Chain, Alg ebraic, and RPN. To execute o ne-number functions, wit h a nu mber displayed, press the k ey or key combinatio n corresponding t o the operation you w ish to e xecute. Th e result is displayed on the b ottom line.
Mathematical Calculations 23 For example, to calculate 6 , press 6:n . The r esult of 2.45 is calculated immediately and displayed on the bottom line. The square root s ymbol ( ) app ears on the top line . Note: before do ing any tr igonometric calculations in the Math menu, che ck whether the angle mode is set for degr ees ( Degrees ) or rad ians ( Radians ). You will need t o chan ge the setting if t he active mode is n ot w hat your problem r equires. For more informatio n on the Mode menu and calcu lator sett ings, r efer to the sect ion titled, The M ode Menu: Setting Preferences in Chapter 1 . Table 2-4 lists one-number functions a long with the ir corresp onding keys. Table 2- 4 Shift ed Function Mat hematical O perations Keys Description :p Calculates sine. :q Calculates cos ine. :r Calculates t angent. :k Calculates nat ural log. :l Calculates nat ural exponent to th e power of x . :m Calculates squ are of x . :n Calculates squ are root. :f Executes th e Random function. Returns a random number in th e range 0 < x <1. :g Calculates f actorial of x (where -253 < x ≤ 253). The Gamma function is used to c alculate x! f or non-integers or negative numbers. :h Calculates y to the x power. :i Calculates t he reciprocal. :d In Chain or Algebraic mode, recalls the result o f the last operation. In RPN mo de, returns t he content of the Last Number variable. :e Rounds x internally to t he number spec ified by the disp lay format. The Math :s Menu There are additional fun ctions available in the Math menu. To open th e Math men u, press : s . See Figure 8 for the menu map of the Mat h menu.
Mathematical Calculations 24 Figure 8 The Menu Map for the Math Menu Press < to scroll t hrough the menu items, starting with Trigonometry. The Trigonometry, Hyperbolic, and Probability items have sub-menu s. Press I w ith the se items displayed to ac cess the functi ons within t he sub men us. Press O to cancel the Mat h menu and return t o current work. Press :s to retur n to the t op of t he Math menu. For an example using the math menu to calculate Sin -1 (0.5), see Table 2-5.
Mathematical Calculations 25 Table 2- 5 Math Menu Example Keys Display Description .5I :s Enters 0.5 a nd opens the Math menu st arting with Trigonometry . I< Selects the Trigonometry sub-menu and scro lls to Sin -1 . Note t he value for Sin -1 is calculated immediate ly and displayed. I or = Validates the result. In the Ma th menu, PI does not perform calculations; it enter s PI for calculations. Y ou may start an operat ion, use the Math menu to ex ecute a f unction, and continue c alculating with your ori ginal operation without losing your w ork. The Probability Sub-menu Lower Tail N ormal Distrib ution (LTND) calculates the probabilit y for a nor mally distributed, r andom variable to be less tha n the input. Inverse Lower Tail Nor mal Distributio n (LTND -1 ) i s t he inverse f unction for LTND; it calculates the value (V) f or which the probability of a normall y d istributed, r andom vari able to be less than V is th e given inp ut. Student, In verse Stu dent, Chi 2 , Inverse Chi 2 , F-Distribution and Inverse F-Distribution perform similar o perations for Studen t, Chi 2 , and F-D istributions. Student, Chi 2 , and F-D istribution a nd their inver se oper ations are special cases, as they requ ire more t han on e number as input. Student and Ch i 2 require (N ), the n umber of deg rees of fre edom, and F-Distribution r equires (N1) an d (N2), two degr ees of freedom. To perform Student and C hi 2 operations or their inverse: 1. Enter the number of de gree(s) of f reedom by typing the number and pressing I or =. 2. Type the number for which you want to calculate the probability, or, for the inverse, the probability for which you want the number. 3. Navigate to t he appropri ate function in the Prob ability sub-me nu of th e Math men u. To perform F-Distribution operations or t heir inver se: 1. Enter t he two degrees of freedom by typing each number followed b y I or =.
Mathematical Calculations 26 2. Type the number for which you want to calculate the probability, or, for the inverse, the probability for which you want the number. 3. Navigate to t he appropriate function in the Probabilit y sub-menu of t he Math menu . Table 2- 6 Probabilit y Exa mple Keys Display Description 10I 8I :s Enters 10 degrees of freedom and the number fo r which probability is to be c alculated. Opens the Math m enu. <<I <<<< Selects the Probability menu item and scrolls to Chi 2 . I or = Validates the result. Table 2- 7 Inv erse Probability Example Keys Display Description 10I 0.37 12I :s Enters 10 degrees of freedom and the probability. Opens the Math menu. <<I <<<< < Selects the Probability menu item. Scrolls to Ch i 2-1 . I or = Validates the result. Two-Number Functions Apart from -* /, t he three additional t wo-number fu nctions accessi ble on the keyboard are:  Y x
Mathematical Calculations 27  nCr  nPr Y x is the pow er function, nCr stands for t he number of combinations of n items taken r at a tim e, and nPr stands for t he number of per mutations of n items taken r at a t ime. Combination=   ! ! ! r n r n  Permutation=   ! ! r n n  Perform cal culations with these funct ions in the same way yo u woul d perform calculations with -/ a nd *, but press : to access the secondary fun ction key. For example, to calculate 15 3 : 1. Press 15. 2. Press :h. 3. Press 3= . The resu lts are sho wn Figure 9. Figure 9 In RPN mode, key in the nu mbers first, f ollowed by I, then pres s t he fu nction key. F or example, for the p ower function example above, in RPN press: 15I 3:h. Storing a nd Recalling Numbers The calculator has ten memories av ailable for use during calculations. These memories are number ed from 1-9 and 0. To store a numb er in a memory, pre ss :$, followe d by the k ey represent ing the m emory number. To rec all a numb er stored in a memory, press L followed b y the key representing t he memory number. You can use the stor e and r ecall functions for t hese memori es any time a nu mber is dis played, or w hen you w ish to ent er a num ber. For example, to store 15 in memory 1 , pres s 15 :$1. To rec all the number in memor y 1, press L 1. You can a lso perform operations to numbers stored in m emories. For example, pr ess 5:$ 2 to stor e 5 in memory 2. To add 12 to th e value of memory 2, press 12:$ 2. Later on, during a calcula tion, you c an
Mathematical Calculations 28 press L2 to reca ll memory 2. Note how the new current value stored in memory 2 is 17 , (5 12). -* and / are v alid mathema tical operations f or memori es. To v iew the stored values in memories 1-9 and 0, press :t , f ollowed by < or > repeatedly to scroll through each m emory s tarting with mem ory 1 ( Mem 1 ). Note that in the Memory menu, you can change t he value of any memory by selecting the memory and typing a number followed by the t key. Recall Arithmetic In RPN, t yping 1 2L 2 add s the v alue of memory 2 to the firs t level of the stack, but it w ill not modif y t he stored value o f memor y 2. This is useful, as it "sa ves" one stack level. You can also use -* and / after L . To perform the same operation in Algebraic and Chain modes, pre ss 12 L2 =. Storing a nd Recalling with Time Value of Money (TVM) Keys To store the current number in th e Time Va lue of Money ( TVM) varia bles, pre ss :$ fo llowed by the desired TVM key. To recall th e stored va lue of a TVM variable, press L followed b y the key of the d esired TVM variable. Note: pressing L does not calculate the variable; it re calls the curr ent value. Recalling a Menu Item Value i n a Menu In a menu, you can recall the current value of a men u item. For example, open the Int erest Conversi on menu (IC onv) by pressing :& . With Nom.% displayed, pre ssing 2 *L= re calls the n ominal rate. This feature i s useful when you n eed to insert the conte nts of a menu item into an algebraic o peration. Rounding Numbers All calculations are per formed internal ly with 15- digit precision and are ro unded to 12 digits w hen returning the results. I n certain instanc es, calculat ions are performe d interna lly with greater than 15-dig it precision. W hen displayed, a number is further rounded t o the number of digits aft er t he decimal po int s et by the FIX item in t he Mode menu. The default setting is two d igits to t he right of the decima l point. For more informa tion, refer to t he section titled, The Mode Me nu: Setting Preferenc es in Chapter 1 . Note: the FIX setting onl y affects the display; it does not affect th e actual num bers. Percentages In Algebraic or Chain modes, pre ssing % divides a number by 100. For e xample, pressing 25% returns 0.25.
Mathematical Calculations 29 To find a percentage of a gi ven number, enter the number an d multiply it by the desired perce ntage, followed by =. For example, to f ind 25% of 200, pre ss 2 00* 25%= to return a r esult of 50 . To add or subtract a percentage of a numb er, enter the first numb er, followed by or - an d the per centage f ollowed by % . Finish your cal culation w ith =. For exampl e, to a dd 10% to 50, press 5 0 10% = to return a re sult of 55 . In RPN mode, the % key calculates x % of t he number on Level 2 of the stack, when x is the number on Level 1 of the stack. It does not modify the number on Lev el 2 of t he stack, and thu s allows yo u to perfor m addition or subtraction after pressing % to add or subtract x % from the numb er. For example, 200I 25% returns 50 , but 200 is still on Level 2 of the stack, and pressing - returns 150 , or 200- 25%.
T i m e V a l u e of M on e y 30 3 T ime V alue of Money The examples in the f ollowing se ctions are calculated with the Mode m enu preferen ces in their default settings, unless otherwise noted. For more information a bout basic f eatures and setting pr eferences, see Chapter 1 , Basic Feature s . Time Va lue of Money (TVM) Keys Cash flow dia grams are useful tool s f or analyzing f inancial s ituations, as they hel p you identify t he TVM f unctions needed to resolve your pro blem. A cash f low diagram i s a draw ing with a set of vert ical arr ows arranged o n a horiz ontal lin e. The horiz ontal line repre sents the period of time from th e beginning o f the fi nancing to t he end. The vertical arrows r epresent the money or cash flows at certain times throughout the per iod. The arrow s' length is proportional t o the ca sh flow amount each ar row represents; a longer arr ow indicates a larger amoun t, a shorter ar row, a smaller a mount. Each arrow 's positio n on the line repres ents the time at which the cash flow occurs. The orientation of the arrow , up o r down, repre sents the "d irection" of the cash flow: up f or money received, down for mone y paid out. See Figure 1.
Time Value of Money 31 Figure 1 Cash Flow D iagram Ex ample with Corresponding T VM Keys The TVM func tions of t he cal culator can solve problems w ith at lea st one ca sh flow, and problems in which a ll t he cash flows, except the f irst and last, are of the same value. To solve other types of cash flow s, refer to the sect ion below t itled, Canadian Mortgages: TVM Cana da , or C hapter 4, Cash Flows . Figure 1 i llustrates a ca sh flow diagram and how the d ata in the d iagram corresponds to t he TVM ke ys. For a complete list of keys used f or TVM pro blems, alo ng w ith the ir descripti ons, see Table 3-1.
Time Value of Money 32 To save values for t he TVM vari ables, enter t he desire d number, followed by the correspond ing TVM key. To calculate an unknown val ue, enter al l k nown va lues and press the k ey of th e item yo u want solved. Table 3- 1 TVM Keys Keys Description N Stores or calculates the number of paymen ts or compounding p eriods. ^ Multiplies a value by the number o f payments per year and stores as N . Y Stores or calculates the nominal, annual interest rate. V Stores or calculates the present value (PV). To a lender or borrower, PV is the amount of a loan ; to a n investor, PV is the initial in vestment. PV always occurs at the beginning of the first p eriod. M Stores or calculates the amount of each periodic payment. [ Stores the n umber of payments or com pounding periods per ye ar. F Stores or calculates the future value (FV), a final cash flow. FV always occurs at the end of the last com pounding period. ? Sets Begin mode (Beg). Payments occur at the b eginning of each compounding period. ] Sets End mode (End). Payments occur a t the end of each com pounding period. Calculating Payments on a Lo an You borrow 140,000.00 f or 30 years (360 months) at 6.5% annual interest, c ompounded mont hly. W h at is your monthly payment to the lender? Note: at the end of the 30 years, you ex pect to have a zero balance ( FV=0). Table 3- 2 TVM Example Keys Displ ay Desc ription 12:[ Inputs 12 as the n umber of payment s per ye ar, or compounding periods per year. 360 N Inputs 360 as the n umber of payments over 30 years. 6.5 Y Inputs 6.5% as the nominal in terest rate p ercentage per yea r. 1400 00V Inputs the p resent value o f the loan at the t ime of the first payment. Th is value is pos itive ( ); it is money yo u receive. 0F Inputs 0 as the future value of the loan (the rema ining balance).
Time Value of Money 33 Table 3- 2 TVM Example Keys Displ ay Desc ription M Returns th e monthly payment. This result is n egative (-); it is money you pa y out. To reset the TVM vari ables to their default va lues, with any TVM v ariable d isplayed press :x. Press < or > repeatedly un til TVM displays. Press I to reset the T VM values, or press O to cancel. Amortization Refer to Figure 2 for a menu map of the Amortization menu ( Amort). Table 3- 3 lists t he keys and variables of the Amortization menu. To open the me nu, press A. The Amortizati on menu cal culations are b ased o n values s tored in th e following TVM registers: N , Y, V , M and [ . To enter v alues for th e TVM v ariables, enter a number followed b y t he corresponding key. For an a mortization exa mple, see Table 3-4. Figure 2 The Menu Map for t he Amortization Menu Table 3- 3 Amortization Menu It ems Menu I tem/Key Description A Opens the Amortization menu . Nb Period Number of periods to group together in th e amortization calculation. The default va lue is the number of payments p er year defined by the [ key. Start Period on which to s tart amortization. De fault is 1 . If you want to amortize for the second year with 12 payments p er year, enter 13 (the second year starts at the 13 th payment with 12 payments per ye ar). Balance The loan balance at th e end of t he assigned am ortized period. Principal Amount of the loan payment applied to the p rincipal at the end of the amortized period. Interest Amount of the loan payment applied to the intere st at the end of the amortized period.
Time Value of Money 34 Enter the va lues for t he TVM k eys for the example be low. Press A followed by < or > to view t he amort ization schedule. Creating an Amortization Schedule You borrow 140,000.00 f or 360 months at 10% interest. Create an amortization schedu le f or the loan. How much interest did you pay for the first year? W hat is the balance of your loan af ter the first year? See Table 3- 4. T he example below is shown with RPN as the active operating mode. Table 3- 4 Amortization Example Keys Display Description 12: [ Inputs 12 as the number of paym ents per year. 30: ^ Inputs 360 (30 times 12 payments per year) as the number of payments for the 30-year loan. 10Y Inputs 10 as the interest rate percentage per yea r. 1400 00V Inputs the value of the loan at the time o f the first payment. 0F Inputs 0 as the future value of the loan (zero balance). M Calculates the monthly payment. A Displays the number of periods to grou p together in the amortization schedule. Default is th e current value of P/YR. < Displays the first period of the grou p of periods to amortize. < Displays the current balance remaining after t he first year. < Displays the current amount of the p rincipal applied towards the loan for the first year. < Displays the amount of interest paid on the loan for the first year. Th e amount of you r payments applied towards interest for t he first year is about 14 ,000.00. < Displays the first payment in the next period to amortize (the second ye ar). Note that the calculator automatically updates Start to the nex t group of periods to a mortize.
Time Value of Money 35 To res et the menu items t o t heir default values, with any item of the Amortization menu disp layed pres s :x . W i th TVM displayed, press I . At t he TVM Reset pr ompt, press I t o reset, or O to cancel. Interest Conversion Menu Figure 3 The Menu Map for the Interest C onversion M enu To open the Interest C onversion m enu (IConv) press :& . Table 3- 5 Inter est Convers i on Menu Items Item Description Nom.% Nominal interest rate: the s tated annual interest r ate compounded as represented by P/YR , such a s 18% compounded monthly ( P/YR=12 ). Eff.% Effective annual interest rate taking compounding into account. C/YR Compounding periods per year. De fault is 12 . Using the I nterest Conversion M enu Find the effective rate of a 36.5% nominal rate compounded daily. See Table 3- 6. See Figure 3 for help with navigating through t he menu. Table 3- 6 Inter est Rate Conversion Example Keys Displ ay Desc ription :& Opens the IConv menu, st arting with the current value of the nominal percentage rate. 36. 5I Inputs 36.5 as the n ominal percentage rate. > Scrolls to compounding periods p er year, C/YR . Default v alue is 12 .
T i m e V a l u e of M on e y 36 Table 3- 6 Inter est Rate Conversion Example Keys Displ ay Desc ription 365 I Inputs 365 as the value for the number of c ompounding periods per year. >= Scrolls to the va riable for the effec tive rate and c alculates it. A 36.5% nominal rat e compounded d aily equals an effective rate o f 44.03%. Note: C/YR i s the same nu mber as P/ YR i n TVM calculations, sinc e most in terest calcula tions are bas ed on the same numb er of payments a nd compoun ding periods p er year, and intere st rate convers ions ar e commonly linked to a subsequent TVM calculation. Th is feature is provided for your co nvenience, but this me ans modifyi ng one numb er also mo difies the other. If your TVM problem requ ires different values for P/YR a nd C /YR, refer to the section below titled, Canadian M ortgages: TVM Canada . The IConv me nu perm its you to s olve for C /YR, but t he result is not a lways a p ositive integer. TVM calculations, however, require C/YR to be an integer larger than z ero. If y ou attempt to perform a TVM calculation w ithout a valid value for C/YR or P/YR, an invalid P/YR error ( ER: I nvalid P/YR) will occur. If you set C/YR to 0 , the re sulting interest conversions are calculated assuming a continuous compounding. As stated ab ove, 0 is not a valid value f or P/YR or C/YR when used in T VM calculations, an d you w ill have to re set it t o a vali d value b efore performing TVM calculations. To res et the menu items t o t heir default values, with any item of the I nterest Convers ion menu displa yed press :x. W ith IC onv displayed, press I to r eset, or O to cancel. To exit t he menu, press O once again. Canadian Mortgages: TVM Canada Figure 4 The Menu Map for the P/YR M enu In Canada, interest rate s for mortga ges are, b y law, g iven as a nominal interest rate, compounded twice yearly. This means that the compounding per iod for the per-period interest rate calculation d iffers from the compoun ding period used to c alculate the nominal rat e. By default, th e HP 20b perform s calculations assuming that the number o f compou nding periods always equ als t he numb er of payments per year. Yo u can, ho wever, enable the TVM Canada option in the Mo de menu, wh ich enables y ou to select the number of co mpounding pe riods per year. For more informat ion, refer t o Chapter 1, Basic Features .
Time Value of Money 37 With TVM Canada enabled in t he Mode menu, the following TVM features change: 1. The P/YR key, :[ , now op ens a menu w ith two items, P/YR a nd C/YR , in w hich you c an specify the number of payments an d compound ing periods per year. Press < or > to scroll thro ugh the menu. See Figure 4. 2. To change t he value of an it em, with the item di splayed, enter t he number desired fo llowed by I. 3. In the I nterest Convers ion menu, th e C/YR item has the same value a s the C /YR item in the P/ YR menu, and C/YR and no longer a ffects P /YR. 4. Note, howev er, if you now cha nge the value of P/YR, the calculator autom atically sets C/Y R so it equals your new value assigned t o P/YR. This means t hat if you modify P/ YR, you also ne ed to m odify C/YR, if P/YR a nd C/YR are different va lues in your TVM prob lem.
Time Value of Money 38 Canadian Mortgage Example Calculate the monthly pa yment for a 25-year (N=300) Canadian mortgage valued at 350,000.00, if the nominal interest rate is 6.0%, compounded t wice yearly (C/YR= 2) with 12 payments per year ( P/YR). Table 3- 7 Canadian Mortgage Example Keys Displ ay Desc ription :u Opens the Mo de menu, st arting with the current FIX value (number o f digits to the right of the decimal p oint). >I Scrolls to TVM mode and sets mod e to TVM Canada . O Returns to default calculator scre en. :[12 I<2 I Opens P/YR m enu. Inputs 1 2 for P/YR a nd 2 for C/YR. O300N 6Y350 00V Exits menu and inputs v alues for N, I/YR, and PV. M Calculates the monthly payment as required by the example . To reset the menu, pr ess :x. With TVM displayed, pr ess I . At th e TVM Re set prompt, pr ess I to reset, or O to canc el. To exit t he menu, pr ess O once ag ain. With the menu set to its default settings , P/YR and C/YR are both set to 12 pa yments/compound ing period s pe r year.
C as h F lo w s 39 4 Cash Flows Figure 1 Cash Flow Diagram In the c alculator, a cash flow list is a set of num bered pair s, CF(n) and #CF(n) , where n is the inde x of th e cash flow list. Each pair represents one or more cas h flows i n a cash f low diagram. As with TVM probl ems, it helps to sketch a cash flow diagram as a first step in solving cas h flow problem s. For some example s of cash flow diagr ams, see Figure 3 at the end of this chapter. CF(n) represents the monetary value of t he cash f low; #CF(n) represents the number of consecutive occurrences of that cash flow. By def ault, #CF(n) is equal to 1 , as most cash flows occur only once. However, in cases where a ca sh f low is r epeated multiple times, using #CF(n ) instead of enter ing the c ash flow value multiple times sa ves calculation time and m emory space in the calculator. To enter a cash flow list, pres s C t o open t he cash f low menu. For each cash flow item, f irst e nter the monetary value followed b y I, then enter t he number of occurrences followed by I. If a ca sh f low occur s o nce, you do not need to t ype 1I . Simply press I or < as 1 is t he d efault.
Cash Flows 40 To erase a cash flow list, wi th any ca sh flow displa yed press :x . The number of cash flow s in the list is di splayed on the bottom lin e, along w ith Cash Flow= . At this prompt , press I . You will b e asked to confirm your choice. Either press I t o confirm the r eset, or O to c ancel. Table 4-1 lists the keys used f or cash f low problems. For a cas h flow ex ample, se e Table 4-2. Table 4- 1 Cash Flow Keys Key Description C Opens the c ash flow list. I Inputs new v alues for va riables in the c ash flow list, the Net Present Value (NPV) menu, and the Internal Rate of Return (IRR) menu. >< Scrolls up and down. o Inserts cash flows into a cash flow list. j Removes cash flows from a c ash flow list. RP Opens the Internal Rate of Return (IRR) and Net Present Value (NPV) menus. Cash Flow Example After an initial investment of 80, 000.00, cash flow (0), you ex pect returns over t he next f ive years as follows: Cash Flow Number Cash Flow Amount Occurrences 1 5,000.00 1 2 4,500.00 1 3 0.00 1 4 4,000.00 1 5 5,000.00 5 6 115,000.00 1 Given t his information, calculate the total of t he cas h flows and the int ernal rate of r eturn (IRR) of the investment. Calculate net pres ent v alue ( NPV) and net future value (NFV), assuming an annua l invest ment interest rate of 10.5%. See Figure 1 for the cash flow diagram and T able 4-2 for how to enter t he cash f lows. The example is shown with RPN as the active operating mode.
Cash Flows 41 Table 4- 2 Cash Flow Example Keys Display Description C Opens the cash flow list. 8000 0}I Inputs -80000 as the m onetary value o f the initial cash f low. Note: the s ign of the cash outflow is negative. I Accepts 1 as the n umber of occurrences for CF(0). Displays the current monetary v alue of CF(1). 5000 I Inputs 5000 as the monetary value of CF(1). Displays the current value, 1 , for t he number o f times CF(1) occurs. I Accepts 1 as the n umber of occurrences for CF(1). Displays the current monetary v alue of CF(2). 4500 I Inputs 4500 as the monetary value of CF(2). Displays the current value, 1 , for the number of times CF(2) occurs. I Accepts 1 as the n umber of occurrences for CF(2). Displays the current monetary v alue of CF(3). I Accepts 0 as the mone tary value of CF(3). Displays the current value, 1 , for the number of times CF(3) occurs. I Accepts 1 as the n umber of occurrences for CF(3). Displays the current monetary v alue of CF(4). 4000 I Inputs 4000 as the monetary value of CF(4). Displays the current value, 1 , for the number of times CF(4) occurs. I Accepts 1 as the n umber of occurrences for CF(4). Displays the current monetary v alue of CF(5). 5000 I Inputs 5000 as the monetary value of CF(5). Displays the current value, 1 , for the number of times CF(5) occurs. 5I Inputs 5 for the n umber of occurrences f or CF(5). Displays the current monetary v alue of CF(6).
Cash Flows 42 Table 4- 2 Cash Flow Example Keys Display Description 115000 I Inputs 115000 as the mone tary value of CF(6). Displays the current value, 1 , for the number of times CF(6) occurs. I Accepts 1 as the n umber of occurrences for CF(6). Analyzing Cash Flows The various functions us ed to analy ze cash flow s are l ocated in t he NPV P and IRR R menus. I f you pr ess R or P before entering cash f lows, you wi ll be redirecte d to the cash flow m enu to en ter va lues into the cash flow list. The m enu maps for the I RR and N PV menus are shown in Figure 2. Table 4-3 describes t he items within these menus. Figure 2 The Menu Map for t he NPV and IRR Me nus
Cash Flows 43 Table 4- 3 NPV and IRR Menu It ems Item Description Inv. I% Investment or discount rate. Enter the inv estment rate or discount rate for the cash flow followed b y I. Net PV Net pr esent value. Shows the value of the c ash flows at the time o f the initial cas h flow, disco unting the future cash flows by the value set for Inv. I%. Net FV Net fu ture value. Sh ows the value of the cash flows at the time of the last cash flow, discounting the earlier cash flows by the value se t for Inv. I%. Net US Net unifor m series. Shows the per-period payment of a regular, periodic ca sh flow of equivalent pre sent value to the cash flow list. Payback Payback. Sho ws the number of periods for the investmen t to return valu e. Discounted Payback Discounted Payback. Shows the number of per iods required for the investment to return value if the cash flows are discounted using the va lue set in Inv. I%. Total The sum of a ll the cash flows, equivalent to NPV if I nv. I% is 0 . #CF/Yr The number of cash flows per year. Th e default is 1 . IRR% Internal rate of return. This is the discount rate for the c ash flow that returns a Ne t Present Value of 0 . See Table 4-4 for an example of the NPV and IRR functions usi ng the cash flow e xample in Table 4-2. Table 4- 4 NPV and IRR Example Keys Displa y Description P Opens the NPV menu. 10. 5I Inputs 10.5 for investment rate. < Displays the NPV of the cash flow with the given Inv. I%. < Displays the NFV of the cash flow with the given Inv. I%. < Displays the Net US of the c ash flow with the given interest rate.
Cash Flows 44 Table 4- 4 NPV and IRR Example Keys Displa y Description < Displays the number of periods required for the cash flow to repay th e investment. << Scrolls to the total valu e of the cash flow. R Displays the IRR for the cash flow. Editing Cash Flows In the c ash flow li st, you can view and modify the current mo netary value of a s pecific cash f low, or cash flows. Press < or > repeatedl y t o sc roll through the list. To m odify the displayed entr y, type a new number a nd pres s I. For example, to change the current monet ary value of the cash flow three, CF(3) , in t he example in Table 4-2 from 0 to 200 , with CF(3)= displayed, press 200 followed by I . You can a lso modify t he number of occurrence s of a cash fl ow i n the same manner with #CF(n) displayed. Pressing :j with a cash f low displa yed erases the displayed cash flow. Pressing :o inserts a cash fl ow i nto the list before the di splayed cas h flow.
Cash Flows 45 Sample Cash Flow Diagrams Figure 3 Sample Cash Flow Diagrams
B on ds 46 5 Bonds B Set.Date Mat.Date CPN% Call Yield% Price Accrued Actual/ Cal.360 Annual/ Semi- annual DWN DWN DWN DWN DWN DWN DWN DWN DWN Figure 1 The Menu Map for the Bond M enu The B ond Menu Before you enter the B ond menu, be sure to verify t he date format is set appropriately f or your prob lem. The default sett ing is mm.ddyyyy , but it can be set for dd.mmyy yy . Bond day counts ( 360/365) an d annua l or semiannual coupon pa yment schedules may be set fr om either the Mode menu or t he Bo nd menu. For more inf ormation on set ting the preferences in the Mode menu, see the section tit led, The Mode Menu: Setting Preferences in Chapt er 1 . To open the Bond me nu, pres s B. Press < or > repeatedl y to scroll through t he items s hown in Figure 1. To change th e value of the displayed item, key in a number or a date a nd press I. Once you have entered al l known data, press < or > r epeatedly t o scroll to an unknown item, and press = t o calcu late it. Table 5-1 lists the it ems in the Bond menu. Table 5- 1 Bond Men u It ems Variable Description Settlement Da te Settlemen t date. Displays the current settlement date. Note: input only. Maturity Date Maturity date or call da te. The call da te must c oincide with a co upon date. Displays the current maturity. Note: input only . CPN% Coupon rate s tored as an annual %. N ote: input only.
Bonds 47 Table 5- 1 Bond Men u It ems Variable Description Call Call value. D efault is s et for a ca ll price pe r 100.00 face va lue. A b ond at maturity has a call value of 100% of its face value. Note: input only. Yield% Yield% to maturity or y ield% to call d ate for g iven price. Note: input/output. Price Price pe r 100.00 face va lue for a giv en yield. Note : input/output. Accrued Interest accrued from the last coupon or payment date un til the sett lement date for a give n yield. Note: this item is R ead-only. Actual/Cal.360 Actual (365-day calendar) or Cal.360 (30-day month /360-day ye ar calendar). Press I to tog gle between these options. Annual/Semiannual Bond coupon (payment) frequency. P ress I to toggle between these options. Bond Calculation Example W hat price should you pa y on April 28, 2010 for a 6.75% U.S. Treasury bon d maturing on June 4, 2020, if you want a yield of 4.75%? Assume the bond is calculated on a semiannual coupon payme nt on an actual/ actual basis. See Table 5- 2. The example below is sho wn with RPN as the active operat ing mode. Table 5- 2 Bond C alculation Example Key Display D escription B Opens the Bond menu. > Scrolls to bond coupon (payment) frequency. I Selects semiannua l coupon payment, as required by the example. <4.2 8 2010 I Inputs Ap ril 28, 2010 for the settlement d ate ( mm.ddyyyy format). <6.0 4 2020 I Inputs June 4, 2020 for the maturity date. <6.7 5 I Inputs 6.75% for the value f or CPN% .
Bonds 48 Table 5- 2 Bond C alculation Example Key Display D escription < Displays current call value. Default is 100 . Note: if Call requires ano ther value, key in the number followed by I . <4.7 5 I Inputs 4.75% for Yield% . <= Calculates t he current value for Price . :$1 Stores 115.89 in memory 1. < Displays the current value for accrued interest. L1= Returns th e result for total price (value of p rice value of a ccrued interest). The n et price you should pay for the bond is 118.58. To reset the menu ite ms to their default v alues, with an y item of the Bond menu di splayed press :x. Wit h Bond displayed, press I to reset th e menu, or O t o cancel. Pre ss O again to exit th e menu.
D at e C al c u la t io n 49 6 Date Calculation Figure 1 The Menu M ap for t he Date Calculation Menu The Date Calculation Menu The Date Cal culation menu is u sed to ca lculate the n umber of days between t wo date s, or a second date g iven a number of days from an initial, or final date. To open the Date Calculation menu, press :@. Press < or > repeatedly t o scroll through the items s hown in Figure 1. Before you enter dates, verify the date is set in the format requir ed for your problem. Date and calend ar format s may be set in the Mode me nu. For more inform ation on setting the pref erences in the Mode Menu, see the section tit led, The Mode Menu: Setting Preferences in Chapt er 1 . To change th e value of a disp layed item, key i n a nu mber or a dat e and press I. On ce you have entered al l known data, press < or > r epeatedly t o scroll to the unknown item and pres s = to c alculate it. Date Calculation Example How man y days remain in the 2010 fiscal year if today's date is June 4, 2010? Ass ume t he f iscal year ends on O ctober 31st, and you wish t o calculate the actual number of days (Act ual). Table 6- 1 Dat e Calculation Example Key Display D escription :@ Opens the Date Calculation menu. Note: 2 in the right of the display represents the day of the week. 2 represents Tuesday. 6.04 2010 I Inputs the starting date in the se lected format.
Date Calculation 50 Table 6- 1 Dat e Calculation Example Key Display D escription <10. 3 12010 I Inputs t he ending date in the selecte d format. <= Calculates t he number of ac tual days between the starting and ending dates. To reset the menu ite ms to their default v alues, with an y item of the D ate menu d isplayed press :x. With Date displayed, press I to reset th e menu, or O t o cancel. Pre ss O again to exit th e menu.
B r ea k - ev en 51 7 Break-even Figure 1 The Menu Map for the Break-even Menu The Br eak-even Menu To open the Break-even menu, press :!. To c hange the value of the displayed item, key in a number and press I . On ce you have entered all known d ata, press < or > re peatedly to scroll to the unknown item and pre ss = to cal culate it. The break-eve n function a llows you to study pro blems in volving a profit, when a quantit y of items, wi th a cost to manufac ture and a fi xed price to develop and market, is sold at a given price . See Figure 1. Break-even Example The sale price of an it em is 300.00, t he cost is 250.00, and the fix ed cost is 150, 000.00. How m any units would have to be sold t o make a profit of 10,000.00? Table 7- 1 Break-even Example Keys Display Des cription :! Opens the Break-even menu star ting with the c urrent value for fixed costs. 1500 00I Inputs 150,000 . 00 for fixed cost . <250 I Inputs 250.00 for variable cost per unit . <300 I Inputs 300 . 00 for price . <100 0 00I Inputs 10,000.00 for profit.
Break-even 52 Table 7- 1 Break-even Example Keys Display Des cription <= Calculates t he current value for the unknown item. 3200 units wo uld have to be sold to r eturn a profit of 10,000.00. To reset the menu ite ms to their default v alues, with an y item of the Brea k-even menu displayed pr ess : x. With BrkEven displayed, press I to rese t the menu, or O to ca ncel. Press O aga in to exit the men u.
B u s in es s P r ob l e m s 53 8 Business Problems Figure 1 The Menu Map for the Per cent Calculation ( �lc) Men u The P ercent Calculation Menu Press :# to open the menu. There are f our items in this menu: markup a s a per centage of cost ( Mkup. %C ), m arkup as a per centage of pr ice ( Mkup. %P ) , part as a percen tage of tota l ( Part%Tot. ), and percent cha nge ( %Change ). Th ese items allow you to access sub-me nus. Press < or > rep eatedly to scroll to the desired sub-me nu, then pr ess I to open it. See Figure 1. To change th e value of a disp layed item, key i n a nu mber an d press I . Once you have e ntered all known data, pre ss < or > r epeatedl y t o scroll t o the unkn own item an d pres s = to cal culate it. To return t o the per cent calcu lation menu, fro m anywh ere within the menu or sub-menus, press :#. To exit the menu, pre ss O
Business Problems 54 Note: for bus iness problem s, margi n is based on price; markup is ba sed on cost. The examples belo w are shown with RPN as the active o perating mo de. Percent Calculation Examples See Table s 8-1 through 8-4 for e xamples of calculations i n the �lc menu. 1. Find the m arkup on a n item if the co st pr ice is $15. 00 and the selling pric e is $22.0 0. See Table 8-1. Table 8- 1 Markup Example Keys Display Des cription :# Opens the �lc menu . I Opens the Mkup.%C sub-menu. 15I Inputs 15 for Cost . <22I Inputs 22 for Price . <= Calculates t he value of Mkup.%C for t he given data. 2. Find the perc ent change b etween 20 and 35 with no compound ing. Table 8- 2 Percent Change Example Keys Display Des cription :# Opens the �lc menu . <<< Scrolls to %Change . I Opens the %Change sub-menu. 20I Inputs 20 for Old . <35I Inputs 35 for New . <= Calculates t he current value of %Change for the g iven data.
Business Problems 55 Note: although the examp le in Tabl e 8-2 ca lls for no compounding, y ou may spe cify t he numb er of co mpounding p eriods used in calculations with the Nb Period item in the %Change sub-menu. Nb Period is the n umber of co mpounding periods used in calculations bet ween the o ld value and new value. The default is 1 , but to change the setting, key in a number with Nb Period displayed, follow ed by I. After calculati ng the examp le above w ith no compounding, say, for exa mple, you w ish to c alculate the percent change over six compounding periods: Table 8- 3 Percent Change Example with C ompounding Keys Display Des cription The curr ent value of %Change for t he given da ta. <6I Inputs 6 for the number of c ompounding periods. >= Calculates t he percent change bet ween the old value and t he new value over six compo unding periods. 3. What is 3 0% of 80 ? Table 8- 4 Part % of T otal Example Keys Display Des cription :# Opens the �lc menu . << Scrolls to the Part %To tal menu item. I Opens the Part as %Total sub-menu. 80I Inputs 80 for Total . <30I Inputs 30 for Part. <= Calculates t he value of Part%Total for the given data. To reset the menu ite ms to their default v alues, with an y item of the � lc menu di splayed press :x. Press > or < to scr oll until �lc displays and press Ito reset the menu, or O to cancel. Press O t o exit the menu.
D ep r e c i at i on 56 9 Depreciation Figure 1 The Menu Map for t he Depreciati on Menu The D epreciation Menu Press :\ to open the Depreciat ion menu. To select a depreciation m ethod, press I repeatedly. See Figure 1. Input the values required for the calculation:  Asset life  Start ing date or month of t he deprecation  Cost and salvage values  Declining balance fact or (DecBal and DBXover onl y)  The f irst year for which you want t o view the depreciation s chedule Scroll through the items of the sub-menu for the s elected depreciation method b y pressing < or > repeatedly. To change the v alue of the displa yed it em, key in a numb er and pre ss I. For the Start item, enter eith er a number or an actual date, d epending on the type of depreciation selected. Pr ess < repea tedly to view the depreciation s chedule.
Depreciation 57 Note: pres sing < on the last it em of a s ub-menu returns you t o the Year it em, not t o the top of the s ub-menu (see Figure 1). By scrolling through all the items of a sub-menu, you incrementall y advance the Year item . This allow s you to see th e depreciation sche dule for t he next y ear without ad ditional entries . Brief description s of the m ethods u sed to c alculate dep reciation are provided in Table 9-1. Table 9-2 describes th e items found in th e depreciatio n sub-menus. For an e xample calculatin g depreciation using the straight-line met hod, see Table 9-3. Table 9- 1 Depreciation Methods Depreciation Method Description Sline Straight line is a m ethod of calculating depreciation presuming a n asset loses a certain percentage of its value a nnually at an amount evenly distributed throughout its u seful life. SOYD Sum-of-the-years' digits is an ac celerated depreciation method. In SOYD, the depreciation in year Y is (Life-Y 1)/SOY/100% of the asset, where SOY is the sum-of-the -years for the asse t, or, for an asset with a 5 -year life, 5 4 3 2 1=15. DecBal Declining balance is an accelerated depreciation meth od that presumes an asset will lose the m ajority of its value during t he first f ew years of its useful life. DBXover Declining balance cr ossover is an accelerated depreciation me thod that presumes an asset will lose the m ajority of its value in the first fe w years of its useful life, but th at it will revert to a consistent depreciation during the latter part of its life, wh ich is th en calculated using the straight line meth od. French SL Straight line Fr ench. This me thod of depreciation is similar to t he Straight line method, except an actual calendar da te in the selec ted format is entered in for Start to indicate when the asset was first placed into ser vice. Amort F French amortizat ion. This method is an accelerated depreciation method with a crossover to the French Straight Line met hod. Table 9- 2 Depreciation Menu Items Item Description Life The exp ected useful life of the asset in years. Start Start refers to t he date or month in which the asset is first placed into service. Dep ending on the type of depreciation, t his can be the month (1-12), or, in the c ase of F rench Straight-line and Amort F, the actual date in the selected format. Note: for non-French depreciations, if the asset were placed into ser vice in the middle of March, for e xample, you w ould enter 3.5 for Start . Cost The depreciable cost of the asset at acquisition.
Depreciation 58 Table 9- 2 Depreciation Menu Items Item Description Salvage The salvage v alue of the asset at the end of its useful life. Factor Th e declining balance factor as a percentage. This is used for declining balance and declining b alance crossover me thods o nly. Year Year for which you want to c alculate the depreciation. Depreciation Depreciation in the given yea r. R.Book Value Remaining book v alue at th e end of the given yea r. R.Depreciable Value Remaining d epreciable value at t he end of the given year. Depreciation Example A metalworking machine, purchased f or 10,000.00, is to be depreciated ov er five years . Its salvage value is estimated at 500.00. Using the straight-line method, find the depreciation and remaining depreciable value for each of the first t wo years of the machine's life. See Table 9-3. Table 9- 3 Straight Line Depreciation Example Key Display D escription :\ Opens the Depreciation menu star ting with the straight line metho d. <5I Inputs 5 for the usefu l life. < Displays the current value of Start . 1 (January) is t he default value. For this example, this value remains unchanged, sinc e the depreciation of the mach ine starts January 1 st ( 1.00 ). <100 0 0I Inputs 10,000.00 for the cos t of the item . <500 I Inputs 500 . 00 for the s alvage value of the item . < Year f or which to calculate the d epreciation. Year 1 is the default value. To c alculate for a ye ar other than 1 , type a number and press I. < Depreciation of the asset in year o ne.
Depreciation 59 Table 9- 3 Straight Line Depreciation Example Key Display D escription < Remaining b ook value after year one. < Remaining d epreciable value after ye ar one. < The nex t year for which to c alcul ate the depreciation. To calculate for a year other than 2 , type a number and press I. < Depreciation of the asset in year two . < Remaining b ook value after year two. < Remaining d epreciable value after ye ar two. To reset the menu ite ms to their default v alues, with an y item of the D epreciation menu displayed pre ss :x. With Depreciation displayed, press I to re set the menu, or O to cancel. Pre ss O to e xit the menu.
S t at is t i c al O pe r at io ns 60 10 S tati stical Operations Figure 1 The Menu Maps for the Data and Statistics Menus
Statist ical Operations 61 The Data and Stats Menus Statist ics analysis funct ions are loc ated in t he Data and Statistics menus accessible with the :y and :z key s. See Figure 1 for ass istance with navigating through the men us. Press :y to ope n the Data menu. In t his menu, enter a l ist of x values for o ne-variable statistics, a lis t of pa irs, (x, F) for weighted, one-variable statistics, a list of numb ers x for one- variable stat istics, or a list of pa irs, ( x, y) for t wo-variable statistics. To enter data, key in a number a nd press I . Press :z to analyze the data. If yo u attempt to open the St atistics (S tats) menu bef ore entering data, yo u will be redirected to the Data menu. When opened, the Stats menu display s 2 Var s for two-variable statistic s. Press I repeatedly to select the t ype of statistical operat ions des ired, two-variable , ( 2 Var s ) , one-variable , (1 Var ), or on e-variable weighted ( 1 Weight ). After sele cting t he type of statist ical operation y ou want, select a sub-m enu b y pre ssing < or > , an d press I to open it. Onc e in a sub-menu, press < or > rep eatedly to v iew the resu lts. To return from t he sub-menu t o the Stat istics menu, pres s :z. Note: in one-variable modes, there are no items for y and the Predictions sub-menu is n ot available. Pressing I with the Predictions sub-menu di splayed open s a sub-menu, in which yo u can choose among six diff erent types of regr ession li nes. See Figure 1. To select a sp ecific type of regre ssion line in the Predictions sub-menu, pre ss I to cycle t hrough the options. No te: if you press = , the calculator au tomatically s elects the curve that is the be st fit for your data. Once you select a re gression line, press < to see the r egression line parameters and perform predictio ns.
Statist ical Operations 62 Table 10- 1 The Statistics Menu Items Menu I tem Description Nb Ite m Number of items. X Mean Average o f X values. Y Mean Average o f Y values. X Std. Dev Standard d eviation for X: a measure o f how d ispersed the x data values are about the mean. Y Std. Dev Standard d eviation for Y: a measure o f how d ispersed the y data values are about the mean. X Popu lation Dev Population Standard deviation for X: a measure o f how dispersed the X data values are about the mean , assuming the da ta constitutes a complete set o f data. Y Popu lation Dev Population Standard deviation for Y: a measure o f how dispersed the y data values are about the mean , assuming the da ta constitutes a complete set of data. S.E.SamP.X Sample er ror for X: a measure of how dispersed the X dat a values are about the mean sample standard deviation, assuming the data is a sampling of a larger, mo re complete data set. S.E.SamP.Y Sample er ror for Y: a measure of how dispersed the Y dat a values are about the mean sample standard deviation, assuming the data is a sampling of a larger, mo re complete data set. Pred X Predicts X fo r a give n hypothetical value of Y, ba sed upon the m odel calculated to fit t he data. Pred Y Predicts Y fo r a give n hypothetical value of X, ba sed upon the m odel calculated to fit t he data. a The a coefficient for the chosen r egression model, which is the slope for a linear model. b The b coefficient for the chosen r egression model, which is the y-intercept for a linear model. Correlation The correlation coefficient for the given (x , y) data. The correlation c oefficient is a number in the r ange -1 through 1 that m easures how c losely the calculated line fits the data. Covariance A measure of how much two variables change in relation to one a nother. Sigma X The sum o f the x values.
Statist ical Operations 63 Table 10- 1 The Statistics Menu Items Menu I tem Description Sigma Y The sum o f the y values. Sigma X 2 The sum o f the squares of the x values. Sigma Y 2 The sum o f the squares for the y values. Sigma XY The sum o f the products of t he x and y values. Statistics Example Sales f or the last five months are represented by t he pairs of values s hown below, with the month number as x , and the sales values as y. Ent er thes e into the Data menu. Using the St atistics menu f or Predictions, predict sales for m onth seven. W hat is t he linear regres sion line? W hat is t he sum of all the y values? See Tables 10-2 and 10-3. Table 10-2 Months and Sales Month Sales Values 1 150 2 165 3 160 4 175 5 170 Table 10- 3 Stat istics Example Keys Display Description :y Opens Da ta menu. 1I1 50I Inputs values for X(1) an d Y(1). 2I1 65I Inputs values for X(2) an d Y(2). 3I1 60I Inputs values for X(3) an d Y(3). 4I1 75I Inputs values for X(4) an d Y(4).
Statist ical Operations 64 Table 10- 3 Stat istics Example Keys Display Description 5I1 70I Inputs values for X(5) an d Y(5). :z Opens Stats m enu. <I Opens Desc riptive sub-menu. << Displays avera ge y . :z< < I Opens Predictions sub-menu. Note: this example performs calcu lations based on a linear (a*X b) regression line. <7I Inputs 7 as the Prediction X val ue ( month 7). <= Calculates Prediction Y value (sales at month 7). < Displays value f or a : the slope of th e regression line. < Displays current value for b : the y-intercept of the regression line. < Displays value f or Correlation . :z< < <I < Opens Sums sub-menu. Displays the s um of a ll y values ( Sigma Y). To reset the menu ite ms to their default v alues, with an y item of the D ata or Statist ics menus displayed press :x. A t the prompt, Stats , pres s I . C onfirm your choice b y pressing I.
E r r or s 65 11 E rrors Error Messages and Calculator Status Table 11- 1 Error Messages Error Message Status ER: Underflow The c alculation generated an underf low (result of 0). ER: x/0 Division by zero. ER: 0/0 Zero divided by zero. ER: ∞*0 Infinite multiplied b y zero. ER: ∞/ ∞ Infinite divided by infinit e. ER: √/ (x<0) Square r oot of a negative number. ER: LN (0) LN of 0. ER: LN (x<0) LN of a negative number. ER: ATrig(|x|>1) ASIN or ACOS of a number f or which the abs olute value is > 1. ER: 1^ ∞ Attempt ed calculation of 1^ /-Infinite. ER: (x<0)^ ∞ Attempt ed calculation of the infinite power of a negative num ber. ER: ∞^0 Attempt ed calculation of /- ∞ ^0. ER: ∞^ (Frac) Attempt ed calculation of /- ∞ ^ (non-integer y). ER: (x<0)^(Frac) Attempt ed calculation of (-x) ^ ( non-integer y). ER: Out of Bounds Input out of bounds. ER: Inv alid P/YR Returned b y TVM f unctions if payments per year are invalid ( <0 or non-integer ). ER: Inv alid Input Returned if arguments are invalid for any r eason. ER: Inv alid I% Returned b y finance functions if I is ≤ 100%. ER: No Solution Returned w hen there is no solution to the problem. ER: Many or N o Solutions Returned if t here is no solution, or more t han one solution t o the problem.
Errors 66 Table 11- 1 Error Messages Error Message Status ER: Many Solutions Returned w hen there are man y solutions to the problem. ER: Inv alid N Re turned b y TVM/Amort if N is invalid. ER: User Abort Returned b y long functions if user st ops the c alculation prior t o completion. ER: ∞ Result Returned if the result is infinite. ER: Ins ufficient Data Returned b y statist ics functions if there is insufficient data f or analysis. ER: No Payback Returned b y payback function if there is no payback on this problem. ER: Unique solution to IRR Not Found Returned if IRR t ries to calculate a solution but c annot find it. User should supply a new guess… ER: Stack Stack overflow when perf orming c alculations with more than 12 pending operatio ns. ER: Parenthesis: An error linked t o use of parentheses: unmatched, t oo many, et c. ER: Ins ufficient Memory Insuff icient memory t o complete t he operation. ER: No Solution Found No s olution found.
W a r r an t y , R eg u la t or y , an d C on t a c t I n f o r m at i on 67 12 W arr anty , Regulato ry , and Cont act Information Replacing the Batteries Use only fresh batteries . D o not u se rechar geable batt eries. The calcu lator take s t wo, 3- volt C R2032 lith ium batteries. To install a new battery: 1. With the calculator turned o ff, slide t he back co ver off. 2. Remove one of the old batterie s and repla ce it with a new bat tery with th e positive polarity symbol facing outward. 3. Remove the se cond batt ery and re place it wit h a new battery wit h the pos itive polarity symbol fa cing o utward. 4. Replace the back cover. Warning! There is danger of explosion if the battery is incorr ectly replaced. Replace only with the same or equivalent type recommended by t he manufacturer. Dispose of used batteries according to the manufacturer's instructions. Do not mutilate, puncture, or dispose of batteries in fire. The batt eries can burst or ex plode, releasing hazardous chemicals. HP Limited Hardware Warranty and Customer Care This HP Limited War ranty gives you, the end-user custo mer, express limited warran ty rights f rom HP, the manufacturer. Please ref er to HP’s Web site for an extensive description of your limited warranty entitlements. In addition, yo u ma y also h ave other legal rights unde r applicable local law or special written a greement with HP. Limited Hard ware Warranty Period Duration: 12 months total (may var y by region , please v isit www.hp.com/support fo r latest information) General Terms HP warran ts to you, the end-user customer, that HP hardware, accessories and supplies will be f ree f rom defects in m aterial s and workmanship after the date of purchase, fo r the period specified above. If HP re ceives notice of su ch defects dur ing the warranty p eriod, HP will, at its option, either repair or replace products which prove to be d efective. Replacement products may b e either n ew or like-new. HP warran ts to you t hat HP sof tware will not f ail to e xecute its programming inst ructions after t he date of purchase, for t he period sp ecified above, due to defects in material and workmanship when properly installed and used. If HP receives notice of s uch defects during the warranty period, HP will replace software media which does not execute its programming inst ructions due to s uch defects. HP does not warrant t hat the operation of HP products will be u ninterrupted or error free. If HP is un able, within a reasonable time, to repair or rep lace any product to a condition as warranted, you will be entitled to a refund of the purchase price u pon prompt re turn of the p roduct with proof of purchase. HP prod ucts may contain remanufactured parts equ ivalent to new in performance or may have been subject to incidental use. Warranty does n ot apply to defects resulting f rom (a) improper or inadequate maintenance or calibration, (b) software, interfacing, parts o r supplies not supplied by HP, (c) unauthorized m odification or misuse, (d) o peration outside of the published environmental specifications fo r the product, or (e) improper site pr eparation or maintenance . HP MAKES NO OTHER EX PRESS W ARRANTY OR CONDITIO N WHETHER WR ITTEN OR OR AL. TO THE E XT ENT ALLOWED BY LOCAL LA W , ANY IMPLIED W ARRANTY O R CONDITIO N OF MERCHANTABILITY, SATISF ACTORY QUALITY, OR FITNESS FO R A PARTICULAR PURPOSE I S LIMITED TO THE DURATION OF THE EX PRESS W ARRANTY SET FORTH ABOVE. Some countries, states or p rovinces do not allow l imitations on the d uration of an implied warranty, so the above limi tation or exclusion m ight not a pply to you. This warranty gives you spec i fic legal rights and you might also have o ther rights that vary from cou ntry to country, sta te to state, or p rovince to province. TO THE EXTENT ALLOWED B Y L OCAL L AW, THE R EME DIES IN THIS WARRANTY STATEME NT ARE YOUR SOL E AND E X CLUSIVE REMEDIES. E XC EPT AS INDICATED ABOVE, IN NO E VENT W ILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS O F DATA OR FOR DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLUDING LOST P ROFIT OR DATA), O R OTHER DAMAGE, W HETHER BASED IN CONTRACT, TORT, OR O THERWISE. Some c ountries, States or p rovinces do not allow the exclusion or limitation of incidental or consequential damages, so t he above limitation or exclusion ma y not app ly t o you. The o nly warranties for HP products and services a re set forth in the express warranty statements accompanyi ng such products and services. HP shall not be liable for technical or editorial errors or omissions conta ined herein. FOR CON SUMER TRANSACTIONS IN AUSTRALIA AND NE W ZEALAND: THE W ARRANTY TERMS CONTAINED IN THIS STATEMENT, EX CEPT TO THE E XTENT LAWFULLY PERMITT ED, DO NOT EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MAN DATORY STATUTORY RIGHTS APPLICABLE TO T HE SALE OF THIS PRODUCT TO YOU.
W arranty , Regulatory, and Contact Information 68 Customer Care In addition to t he one year hardware warranty your HP calculator also c omes with one year of technical suppor t. If you need assistance, HP customer care can be reached by either email or telephone. Before calling please locate t he call center nearest you from the list below. Have you r pr oof of purchase and calculator serial number ready when you c all. Telephone numbers are subject t o change, and local and national telephone rat es may apply. For more support information, please v isit the web at : www.hp.com/support . Contact Inf ormation Table 12-1 Conta ct Information Country/Region Contact Africa (English) www.hp.co m/support Afrique (fran çais) www.hp.co m/support Argentina 0-800-555-5000 Australia 1300-551-664 Belgique (franç ais) 02 620 00 85 Belgium (English) 02 620 00 86 Bolivia 800-100-193 Brasil 0-800-709-7751 Canada 800-HP-INVENT Caribbean 1-800-711-2884 Č eská republikaik 296 335 612 Chile 800-360-999 China 中国 010-68002397 Colombia 01-8000-51-4746-8368 Costa Rica 0-800-011-052 4 Denmark 8 2 33 28 44 Deutschland 069 9530 7103 Ecuador 800-711-2884 El Salvador 800-6160 España 913753382 France 01 4993 9006
W arranty , Regulatory, and Contact Information 69 Table 12-1 Conta ct Information Country/Region Contact Greece Ελλάδα 210 969 64 21 Guatemala 1-800-999-5105 Honduras 800-711-2884 Hong Kong 香港特 別行政區 852 2833-111 1 India www.hp.com/support/indi a Indonesia 65 6100 6682 Ireland 01 605 0356 Italia 02 754 19 782 Japan 日本 81-3-6666-9925 Korea 한국 www. hp.com/support/korea Magyarország www.hp.co m/support Malaysia 65 6100 6682 México 01-800-474-68368 Middle East Internati onal www.hp.co m/support Netherland 020 654 5301 New Zeal and 0800-55 1-664 Nicaragua 1-800-711-2884 Norwegen 23500027 Österreich 01 360 277 1203 Panamá 001-800-711 -2884 Paraguay (009) 800-541-0006 Perú 0-800-10111 Philippines 65 6100 6682 Polska www.hp.co m/support Portugal 021 318 0093
W arranty , Regulatory, and Contact Information 70 Table 12-1 Conta ct Information Country/Region Contact Puerto Rico 1-877 232 0589 Russia Росси я 495 228 30 50 Schweiz (D eutsch) 01 439 5358 Singapore 6100 6 682 South Afric a 0800980 410 South Korea 한국 2-561-2700 Suisse (français) 022 827 8780 Suomi 09 8171 0281 Sverige 08 5199 2065 Svizzera (italiano) 022 567 5308 Türkiye www.hp.com/support Taiwan 臺灣 852 28052563 Thailand ไทย 65 6100 6682 United Kingdom 0207 458 0161 United States 800 -HP INV ENT Uruguay 0004-05 4-177 Venezuela 0-800-474-68 368 Viêt Nam 65 6100 6682
W arranty , Regulatory, and Contact Information 71 Product Regulatory & Environment Information Federal Communications Commission Notice This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, us es, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. I f this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures:  Reorient or relocate the receiving antenna.  Increase the separation between the equipment and the receiver.  Connect the equipment into an outlet on a circuit different from that to which the receiver is connected.  Consult the dealer or an experienced radio or television technician for help. M o di f i ca ti o n s The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by Hewlett- Packard Company may void the user’s authority to operate the equipment. Declaration of Conformity for products Marked with FCC Logo, United States Only This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: (1) this device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation. If you have questions about the product that are not related to this declaration, write to Hewlett-Packard Company P.O. Box 692000, Mail Stop 530113 Houston, TX 77269-2000 For questions regarding this FCC declaration, write to Hewlett-Packard Company P.O. Box 692000, Mail Stop 510101 Houston, TX 77269-2000 or call HP at 281-514-3333 To identify your product, refer to the part, series, or model number located on the product. Canadian Notice This Class B digital apparatus meets all requirements of the Canadian Interference-Causing Equipment Regulations. Avis Canadien Cet appareil numérique de la classe B respecte toutes les exigences du Règlement sur le matériel brouilleur du Canada. European Union Regulatory Notice This product complies with the following EU Directives:  Low Voltage Directive 2006/95/EC  EMC Directive 2004/108/EC Compliance with these directives implies conformity to applicable harmonized European standards (European Norms) which are listed on the EU Declaration of Conformity issued by Hewlett-Packard for this product or product family.
W arranty , Regulatory, and Contact Information 72 This compliance is indicated by the following conformity marking placed on the product: This marking is valid for non-Telecom products and EU harmonized Telecom products (e.g. Bluetooth). xxxx* This marking is valid for EU non-harmonized Telecom products . *Notified body number (used only if app licable - refer to the product label) Hewlett-Packard GmbH, HQ-TRE, Herrenberger Srasse 140, 71034 Boeblingen, Germany Japanese Notice Perchlorate Material - special handling may apply This calculator's Memory Backup battery may contain perchlorate and may require special handling when recycled or disposed in California. Disposal of Waste Equipment by Users in Private Household in the European Union Chemical Substances HP is committed to providing our customers with information about the chemical substances in our products as needed to comply with legal requirements such as REACH ( Regulation EC No 1907/2006 of the European Parliament and the Council). A chemical information report for this product can be found at: http://www.hp.com/go/reach This symbol on the product or on its packaging indicates that this product just not be disposed of with your other household waste. Inst ead, it is your r esponsibilit y to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment. The separate col lection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment. For more information about where you can drop off your wa ste equipment for recyclin g, please contact your local city offic e, your household waste disposal service or the shop where you purchased the product.
W arranty , Regulatory, and Contact Information 73 产品中有毒有害物质或元素的名称及含量 根据中国《电子信息产品污染控制管理办法》 有毒有害物质或元素 部件名称 铅 ( Pb) 汞 ( Hg) 镉 (Cd) 六价铬 (Cr(VI)) 多 溴联 苯 (PBB) 多溴二苯醚 (PBDE) PCA X O O O O O 外觀殼子 /字鍵 O O O O O O O ：表示该有毒有害物质在该部件所有均质材料中的含量均在SJ/T11363-2006 标准规定的限量要求以下。 X ：表示该有毒有害物质至少在该部件的某一均质材料中的含量超出SJ/T11363-2006 标准规定的限量要求。 表中标有 “X” 的所有部件都符合欧盟 RoHS法规 “ 欧洲议会和欧盟理事会2003 年1 月27 日关于电子电器设备中限制使用某些有害物质的2002/95/EC 号指令” 注：环保使用期限的参考标识取决于产品正常工作的温度和湿度等条件
I nd ex 74 Index ! !: key, 2 3 % % c hange, 53 % yield, 47 = =: k ey, 12 A a: s lope, 62 absolute v alue. See Math menu Algebraic mode, 17 amortization: Amort k ey, 33; exampl e, 34; menu items, 33 annual: bond, 47 annunciators, 11 ANS. See last number B b: y-intercep t, 62 backspace k ey, 16 balance: amortization, 33 begin mode : Beg key, 32 bond: annual, semiannual, 10; example, 47; key, 46; menu items, 46 bonds, 46 bottom line: display, 8 break-even: BrkEv key, 51; e xample, 51 business problems, 53; pe rcent calculation e xa mples, 54 C calculation mode : Chain, Algebraic, a nd RPN , 10 calendar: Ac tual, Cal.360, 10 call value, 47 Canada TVM example, 38 Canadian TVM, 36 cash f low: example, 40; keys, 40; sample diagrams, 45 cash f lows, 39; analyzing, 42; editing, 44; number per year, 43 Chain mode, 17 Chi, 25 clearing. S ee: Reset menu compounding pe riods: N key, 32 compounding pe riods per year: P /YR key, 32 Compounding, per year, 35 contents, 3 contrast, 7 correlation, 61, 62 cosine: COS k ey, 23 cost: deprec iation, 58; fixed. See break- even; variab le per unit. See break- even coupon rate, 46 covariance, 61 , 62 CshFl key. S ee cash f low cursor, 7 D Data key. Se e Statistics data menu, 61 date: ac tual, 47; maturity, 46; settlement, 46 Date 1. See Date calculation Date 2. See Date calculation date calcu lation: Date key, 49; example, 49 date format, 9 days between . See Date calculation decimal point, 9 decimal separ ator: point or c omma, 9 default calculato r screen, 8 degrees, 9 delete: DEL key, 44 delete key, 44 deleting. See Reset menu depreciation, 56 ; Depr key, 56; example, 58; methods , 56 descriptive: sub menu. See Statistics menu discounted pa yb ack, 4 3 display, 7; t w o lines , 8 down arrow key. See scroll E EEX key. Se e scientific notation end mode: End key, 3 2 error messages, 65 F factor: d eclini ng bala nce. See depreciation factorial: ! key, 23 F-distribution, 25 Fix: display prec ision. See Mode menu function: on e-number, 22 functions: two-number, 26 future value : FV key, 32 I IConv key. S ee interest conversion INPUT: ke y, 12 insert: INS k ey, 44 interest: accrued. See bonds ; towards loan payment. See amortization interest co nversion: example, 35 interest rate: effective, 35; nomi nal, 35; nominal, I/YR ke y, 32 inverse tail n ormal distribution, 25 IRR: key, 42 K key: highlighting, 11; presses, 11 ; primary function, 11; secondary function, 11 keyboard map, 6 L language: s election, 7 last number , 19; ANS ke y, 19 life. See depreciation line: regress ion, 61 log: LN key. See Math menu logarithmic functions , 23 lower tail nor mal distribution, 25 M markup: as cost, 53; as price, 53 math: M ath key, 23 math functions , 16 Math menu: Absolute value, 24; Hyperbolic, 24; Log, 24; Probability, 24; Trigonometry, 24 mean, 6 1 memory, 13; k ey, 13 menu: Amortization, 33; Bond, 46; Break-even, 51; Cash Flow, 39; Date Calculation, 49; Depreciation, 56; Interest Conve rsion, 35; IRR, 42; Math, 22; Memory, 13; Mode , 8; NPV, 42; Payment p er year, 36; Percent Calculation, 53; Reset, 13; Statistics, 60; TVM, 30; TVM Can ada, 36 menu item v alue: recalling, 2 8 menus: items, types of, 15; maps, 14; special, 13; sub-menus, opening, 14 mode menu: k ey, 7
Index 75 N N key, 3 2 natural exponen t: e to t he power of x key, 23 nCr, 2 7 negative nu mbers, 16 net fu ture value, 43 net present value, 43 net uniform series, 43 nPr, 2 7 NPV: ke y, 42 NPV, IRR: m enu items, 43 number entry , 16 number period: compounding, 55 number periods: amortization, 33 numbers: rounding, 28; storing and recalling, 27 O off: calculator off, 7 Off: key, 7 on: calculator on, 7 On: key, 7 P P/YR: key, 32 parentheses: use in Chain mode, 17 parentheses (swap and roll do wn): ke ys in RPN, 21 payback, 43 percent calculation: % calc k ey, 53 percentage: % key, 28 percentage of total, 53 percentages: simple, 28 periodic payment: PMT key, 32 PI. See Math Menu population, 61 power funct ions, 23 Predictions: su b-menu. See Statistics present value: PV key, 32 price: break-even, 51; face v alue. See bonds; percent calculation, 54 principal, 33 probability, 25 product: x and y values, 63 profit, 51 Q quantity: break-even, 52 R radians, 9 random func tion: RAND key, 23 recall arithmetic, 28 recalling numbers: RCL key, 27 reciprocal: 1/x ke y, 23 regression line, 61 remaining book value, 58 remaining depre ciable value, 58 Reset: k ey, 13 roll down. See RPN rounding numbe rs: RND key, 2 3 RPN: Reverse Polish Notat ion, 18 RPN sta ck, 18 S S.E. SamP. X and Y, 61 salvage: d epreciation, 58 scientific n otation: EEX key, 16 scroll: up and down arrow keys, 8 semiannual: b ond, 47 Sigma X,Y, 61 sign: positive, negative key, 16 sine: SIN key, 23 slope, 61 square of x: key, 23 square r oot key, 23 standard deviation , 61 start: amortization period, 33 start dat e: depreciation, 58 statistics: menu items, 62; on e-variable, 61; one-variable weighted, 61; Stat s key, 61; t wo-variable, 61 statistics e xam ple, 63 stats menu, 61 storing numbers : STO key, 2 7 student, 25 sums: sub -menu. See Statistics swap. S ee RPN symbol: battery, 7 T tangent: T AN key, 23 thousands sepa rator, 9 time value of money: k eys, 32 top line: display, 8 total: cash f lows, 43 TVM: exampl e, 3 2; storing a nd recalling numbers, 28 U up arr ow key. See scr oll X x: Sigma, 62 ; square of Sigma x, 63; times payment per year, xP /YR k ey, 32 x mean, 6 2 x mean sample, 62 x population Std . Dev., 62 x prediction, 62 x standard deviation, 62 Y y: Sigma, 63 ; square of Sigma y, 63 y mean, 6 2 y mean sample, 62 y population Std . Dev., 62 y prediction, 62 y standard deviation, 62 y to th e x power, 23 y-intercept, 61