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iHP 10bII+ Financial Calculator User’s GuideHP Part Number: NW239-90001Edition 1, May 2010

At a Glance...2Shift KeysMost keys on the HP 10bII+ have three functions: • a primary function printed in white on the key. • a secondary function pri

Cash Flow Calculations92Figure 5 Initial cash flow and cash flow groupsWhenever you enter a series of cash flows, it is important to account for every

Cash Flow Calculations93Viewing and Editing Cash FlowsThe cash flow editor application allows you to review entered data quickly to ensure accuracy. I

Cash Flow Calculations946. To replace the currently displayed value, simply type a new number and press Æ. Only valid entries are accepted. If you typ

Cash Flow Calculations95Calculating Net Present Value and Net Future ValueThe net present value (NPV) function is used to discount all cash flows to t

Cash Flow Calculations96How much should you pay for the contract if you wish to yield a yearly rate of 15% on your investment?Figure 6 Cash flow diagr

Cash Flow Calculations97The cash flows that describe your prospective investment are now in the calculator. Press v¤. Press 1 or A to scroll through t

Cash Flow Calculations98Figure 7 Cash flow diagram (Calculates NPV)Automatic Storage of IRR/YR and NPVWhen you calculate NPV, the result is stored in

Calendar Formats and Date Calculations999 Calendar Formats and Date CalculationsCalendar FormatThe calendar options for bonds and date calculations ar

Calendar Formats and Date Calculations1002. Enter the number of digits : through d that you wish to appear after the decimal point. To view the entire

Calendar Formats and Date Calculations101Date Calculations and Number of Days To calculate the date and day, past or future, that is a given number of

At a Glance...3For more information on the calculator’s keys and basic functions, refer to chapter 2, Getting Started.PercentagesAdd 15% to 17.50.Find

Calendar Formats and Date Calculations102To enter the data for this example using the Æ key:Number of DaysUse the \Ä function to calculate the number

Calendar Formats and Date Calculations103Example 2How many days are there between October 17, 2012 and June 4, 2015? Use the M.DY setting and compute

Calendar Formats and Date Calculations104Using the Æ key:Table 9-6 Calculating the actual number of days using the ‘INPUT’ keyKeys Display Description

Bonds10510 BondsThe Bond KeysOn the 10bII+, bond calculations are based on data or settings stored in the ten keys which make up the top two rows of t

Bonds106When entering data for bond calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys

Bonds107Example 2A bond has a call provision at 104 and a coupon rate of 5.5%. If the bond matures on October 15, 2020 and is presently selling at 101

Bonds108Continuing with the same bond problem, assume the bond will not be called. What is the expected yield to maturity?Resetting the bond keysTo re

Break-even10911 B r e a k - e v e nThe break-even function allows you to study problems involving a profit, when a quantity of items, with a cost to m

Break-even110Example 1The sale price of an item is 300.00, the cost is 250.00, and the fixed cost is 150,000.00. How many units would have to be sold

Break-even111Example 2What is the estimated maximum fixed cost you can afford to manufacture 10,000 water filters, if your desired selling price is 45

At a Glance...4If the cost is 20.00 and the markup is 33%, what is the selling price?For more information on percentages, refer to chapter 3, Business

Break-even112Resetting the Break-even keysTo reset the break-even keys to their default values, press ]OY. A brief message flashes on the screen to in

Statistical Calculations11312 Statistical CalculationsThe 10bII+ allows you to enter data for one- and two-variable statistics easily. Once data is en

Statistical Calculations114Clearing Statistical DataClear the statistical data before entering new data. If you don't clear the statistical data,

Statistical Calculations115Figure 3When the calculator switches to register-based mode, some key points to consider:• You may enter an unlimited numbe

Statistical Calculations116Viewing and Editing Statistical Data1. P r e s s v¡to open the editor. The number of items accumulated, n, is displayed,

Statistical Calculations117At what temperature would the manager predict to sell 800 drinks? How many employees will be needed for tomorrow's pre

Statistical Calculations118After modifying the data, predict the next day’s activity at a record 45oC.Table 12-4 Adding more dataKeys Display Descript

Statistical Calculations119Summary of Statistical CalculationsThe STAT annunciator indicates that a statistical calculation was performed. Some functi

Statistical Calculations120Mean, Standard Deviations, and Summation StatisticsYou can calculate the mean ( ), sample standard deviation (Sx), and popu

Statistical Calculations121The standard deviations calculated by \h and \h\« are the sample standard deviations. They assume that the data is a sampli

At a Glance...5Multiply 17, 22, and 25 by 7, storing ‘× 7’ as a constant operation.Store 519 in register 2, then recall it.Store 1.25 into register 15

Statistical Calculations122Linear Regression. Calculate r (the correlation coefficient), m, b, and as follows:1. Clear the statistical registers by p

Statistical Calculations123Figure 4 Diagram on forecasting sales and minutes for advertisingTable 12-10 Example for forecastingKeys Display Descriptio

Statistical Calculations124Estimate what the level of sales would be if the business purchased 7 or 8 minutes of advertising.How many minutes of adver

Statistical Calculations125Regression Models and VariablesThe 10bII+ has six built-in regression models, as well as the ability to calculate which mod

Statistical Calculations126If BEST FIT is selected, the 10bII+ calculates the best fit when \Z, \W, or \T is pressed. When selected, BEST FIT flashes

Statistical Calculations127ExampleUsing five books labeled A, B, C, D, and E, how many different ways can three books be placed on a shelf? Table 12-1

Statistical Calculations128ExampleStore a seed value of 42; set the number display to 9. Then generate three random numbers.Advanced Probability Distr

Statistical Calculations129Normal Lower Tail ProbabilityTo calculate the area under the curve to the left of z (the lower tail probability), enter the

Statistical Calculations130Inverse of Normal Lower Tail ProbabilityFigure 8What is the z-value corresponding to a lower tail cumulative probability of

Statistical Calculations131Student's T Probability Lower Tail Figure 11To calculate the area under the Student's T Distribution curve, first

At a Glance...6Time Value of Money (TVM)Enter any four of the five values and solve for the fifth.A negative sign in the display represents money paid

Statistical Calculations132Inverse of Student’s t Probability Lower TailIf you know the lower tail probability, P, and you want to calculate t, enter

Statistical Calculations133Conversions from Lower TailThe distribution functions on the 10bII+ return values for the lower tail cumulative probability

Statistical Calculations134Example 2The variable Z is a standard normal random variable. What is the probability that z is greater than 1.2 or less th

Statistical Calculations135Example 3The variable Z is a standard normal random variable. Find z so that the probability that Z is less than z and grea

Statistical Calculations136

Additional Examples13713 Additional ExamplesBusiness ApplicationsSetting a Sales PriceOne method for setting the per unit sales price is to determine

Additional Examples138Cost of Not Taking a Cash DiscountA cash discount gives a buyer a reduction in price if the payment is made within a specified t

Additional Examples139Loans and MortgagesSimple Annual InterestExampleYour good friend needs a loan to start his latest enterprise and has asked you t

Additional Examples140To solve a continuous compounding problem complete these steps:1. Compute the annual effective rate using the above equation.2.

Additional Examples141Yield of a Discounted (or Premium) MortgageThe annual yield of a mortgage bought at a discount or premium can be calculated give

At a Glance...7TVM What if...It is not necessary to reenter TVM values for each example. Using the values you just entered, how much can you borrow if

Additional Examples142Step 3Enter actual, current values for N and PV; then find the new I/YR for the discounted mortgage with balloon.Annual Percenta

Additional Examples143Example: Interest-Only Loan With FeeA 1,000,000, 10-year, 12% (annual interest) interest-only loan has an origination fee of thr

Additional Examples144Loan With a Partial (Odd) First PeriodTVM calculations apply to financial transactions where each payment period is the same len

Additional Examples145Automobile LoanExampleYou are buying a new 14,000.00 sedan. Your down payment is 1,500 and you are going to finance the remainin

Additional Examples146The first option costs slightly less.Canadian MortgagesIn Canadian mortgages, the compounding and payment periods are not the sa

Additional Examples147What if … TVM CalculationsOne of the most valuable aspects of the HP 10bII+’s TVM application is the ease with which it handles

Additional Examples148Part 3What if you had monthly payments as in part 1, but chose a 15-year term? What would your new payment be? What would be the

Additional Examples149Figure 20 Cash flow diagramSet to Begin mode. Press \¯ if BEGIN annunciator is not displayed.When compounding occurs only once p

Additional Examples150Then use that PV as the FV on the following cash flow diagram, and calculate the PMT.Figure 21 Cash flow diagram (Calculate PMT)

Additional Examples151account be? Assume that only the interest is taxed (assume the principal was taxed before deposit). What is the purchasing power

At a Glance...8AmortizationAfter calculating a payment using Time Value of Money (TVM), input the periods to amortize and press \Ê. Press \Ê once for

Additional Examples152ExampleIf you invest 3,000 each year for 35 years, with dividends taxed as ordinary income, how much will you have in the accoun

Additional Examples153The payment calculation is a straightforward TVM payment calculation using the new amount as the PV.Set to End mode. Press \¯ if

Additional Examples154N1 = 82CF2 = 861.59N2 = 180 - 82 = 98Net Future ValueThe net future value can be calculated by using the TVM keys to slide the

Appendix A: Batteries and Answers to Common QuestionsIAppendix A: Batteries and Answers to Common QuestionsPower and BatteriesThe calculator is powere

Appendix A: Batteries and Answers to Common QuestionsII7. I n ser t t h e o t h e r n ew ba t t e r y, making sure that the positive sign (+) bat

Appendix A: Batteries and Answers to Common QuestionsIIIThe calculator responds to keystrokes, but you suspect that it is malfunctioning:1. It is like

Appendix A: Batteries and Answers to Common QuestionsIVQ: How can I change the sign of a number in a list of cash flows?A: You must edit or replace th

Appendix B: More About CalculationsIAppendix B: More About CalculationsIRR/YR CalculationsThe calculator determines IRR/YR for a set of cash flows usi

Appendix B: More About CalculationsIITime Value of Money (TVM)Payment Mode Factor: S = 0 for End mode; 1 for Begin mode.AmortizationBAL is initially P

Appendix B: More About CalculationsIIICash-Flow CalculationsWhen NPV = 0, the solution for i% is the periodic internal rate of return.NFV = NPV x SPFV

At a Glance...9For more information on amortization, refer to the section titled, Amortization in chapter 6, Time Value of Money Calculations.Deprecia

Appendix B: More About CalculationsIVBondsReference: Lynch, John J. Jr. and Jan Mayle, Stanford Securities Calculation Methods, Securities Industry As

Appendix B: More About CalculationsVDepreciationFor the given year number (YR) and with Factor (FACT) as a percentage:For the last year of depreciatio

Appendix B: More About CalculationsVIForecastingName FitBest Fit Automatically selects fitLinear m*x+bLogarithm m*ln(x)+bExponentialb*e(m*x)Powerb*xmE

Appendix C: MessagesIAppendix C: MessagesClear MessagesPress M or | to clear a message from the display.Table C-1 MessagesMessage Displayed Descriptio

Appendix C: MessagesIIBOND CLR bond registers were cleared.STAT CLR statistical memory and registers were cleared.Best Fit The calculator selected th

Warranty, Regulatory, and Contact Information117 Warranty, Regulatory, and Contact InformationReplacing the BatteriesWarning! There is a danger of exp

Warranty, Regulatory, and Contact Information2General TermsEXCEPT FOR THE WARRANTIES SPECIFICALLY PROVIDED FOR IN SUBSEQUENT PARA-GRAPHS OF THIS SECTI

Warranty, Regulatory, and Contact Information3OR CONDITION WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL LAW, ANY IMPLIED WARRANTY OR CONDIT

Warranty, Regulatory, and Contact Information4Declaration of Conformity for Products Marked with FCC Logo, United States OnlyThis device complies with

Warranty, Regulatory, and Contact Information5Please refer to the regulatory label provided on the product. The point of contact for regulatorymatters

At a Glance...10For more information on depreciation, refer to chapter 7, Depreciation.Interest Rate ConversionTo convert between nominal and effectiv

Warranty, Regulatory, and Contact Information6Perchlorate Material - special handling may applyThis calculator's Memory Backup battery may contai

Warranty, Regulatory, and Contact Information7El Salvador 800-6160 Equador 1-999-119; 800-711-2884 (Andinatel)1-800-225-528; 800-711-2884 (Pacifitel)E

Warranty, Regulatory, and Contact Information8PeruPerú0-800-10111 Philippines (2)-867-3351PolandPolskawww.hp.com/support Portugal 021 318 0093Puerto R

Warranty, Regulatory, and Contact Information9

Warranty, Regulatory, and Contact Information10

1AAdvance payments 72Algebraic modecalculations 28Amortization 74equations IIrange of payments 76single payment 77TVM keys used 75Angle formatselectin

2In-line functions 37Interestcompound interest 57interest rates 57simple interest 56Interest rate conversions 79Investmentsdifferent compounding perio

3clearing IIMessages Icalculator status 44list of IModesTVM begin and end 62NNegative numbers 29Net future value 95Net present value 95Number of days

At a Glance...11Cash Flows, IRR/YR, NPV, and NFVTable 1-21 Cash flows, IRR, NPV, and NFV keysKeys Description]O:Clears cash flow memory.\ÍNumber of pe

iiLegal NoticeThis manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company mak

At a Glance...12If you have an initial cash outflow of 40,000, followed by monthly cash inflows of 4,700, 7,000, 7,000, and 23,000, what is the IRR/YR

At a Glance...13For more information on cash flows, refer to chapter 8, Cash Flow Calculations in the HP 10bII+ Financial Calculator User’s Guide.Date

At a Glance...14BondsBond calculations, primarily calculating bond price and yield, are performed by two keys, ]Ñ and ]Ô. These keys permit you to inp

At a Glance...15For more information on bond calculations, refer to chapter 10, Bonds.Table 1-27 Bond calculationKeys Display Description]OjBOND CLR (

At a Glance...16Break-evenThe sale price of an item is 300.00, the cost 250.00, and fixed cost 150,000.00. For a profit of 10,000.00, how many units w

At a Glance...17Statistical CalculationsTable 1-30 Statistics keysKeys Description\tClear statistical registers.x-data ¡Enter one-variable statistical

At a Glance...18Using the following data, find the means of x and y, the sample standard deviations of x and y, and the y-intercept and the slope of t

At a Glance...19ProbabilityEnter .5 as a Z-value and calculate the cumulative probability of the Z-value and the Z-value from a given cumulative proba

At a Glance...20Trigonometric FunctionsTable 1-34 Trigonometry keysFind Sin =.62 in degrees. If RAD is displayed, press ]3. Keys Description] c, R, o

At a Glance...21Convert the results to radians using Pi.For more information on trigonometric functions, refer to chapter 2, Getting Started.Table 1-3

iiiHP 10bII+ Financial Calculator

At a Glance...22

Getting Started232 Getting StartedPower On and OffTo turn on your HP 10bII+, press =. To turn the calculator off, press the orange shift key, \, then

Getting Started24Basics of Key FunctionsTable 2-1 Basics of key functionsKeys Display Description= 0.00 Turns calculator on.][blue] 0.00Displays shift

Getting Started25Shift KeysMost keys on the HP 10bII+ have three functions: • a primary function printed in white on the key. • a secondary function p

Getting Started26Simple Arithmetic CalculationsOperating ModesTo change the operating mode, press the blue shift key, ] followed by ? to toggle betwee

Getting Started27If you press an operator key after completing a calculation, the calculation is continued.Calculations in Chain ModeCalculations in C

Getting Started28For example, to calculate 1 + (2 x 3), you may enter the problem as written from left to right, with parentheses to prioritize the mu

Getting Started29Negative NumbersEnter the number and press y to change the sign.Calculate -75 ÷ 3.Understanding the Display and KeyboardCursorThe bli

Getting Started30Clear All\N all clears all memory in the calculator, with the exception of the payments per year (P/Yr) setting. To clear all memory

Getting Started31Table 2-11 Annunciators and statusAnnunciator Status, A shift key has been pressed. When another key is pressed, the functions labele

ivKeyboard Map LegendNumber (row of keys)Primary Functions (white)SHIFT Down \(orange functions on key bevel) SHIFT Up ](blue functions above keys) 1

Getting Started32Input KeyThe Æ key is used to separate two numbers when using two-number functions or two-variable statistics. The Æ key can also be

Getting Started33Time Value of Money (TVM), Cash Flows, Bond, and Break-even KeysWhen entering data for TVM, cash flows, bond, depreciation and break-

Getting Started34The random function]6, and Pi \; are special operators. They insert values for Pi, or a random number in the range 0 < x <1, in

Getting Started35Trigonometric and Hyperbolic Functions and ModesSelecting Angle FormatThe trigonometric angle format determines how numbers are inter

Getting Started36Pi Pressing \; displays the value of . Although the displayed value is appears in the current display format, the 12 digit value is

Getting Started37ExamplePerform the following hyperbolic calculations.Two-Number FunctionsWhen a function requires two numbers, other than for additio

Getting Started38Press M, and now calculate the same example using the Æ key to store the first number, then key in the second number and perform the

Getting Started39The Table 2-23 below lists the two-number functions of the calculator.Two-number functions may be performed in either CHAIN or ALGEBR

Getting Started40Example 2Calculate natural logarithm (e2.5). Then calculate 790 + 4!Example 3The power operator, , raises the preceding number (y-va

Getting Started41Last AnswerWhen a calculation is completed by pressing 4, or a calculation is completed during another operation, the result is store

1Table of ContentsLegal Notice...iiHP 10bI

Getting Started42Regardless of the current display format, each number is stored internally as a signed, 12-digit number with a signed, three-digit ex

Getting Started43Scientific NotationScientific notation is used to represent numbers that are too large or too small to fit in the display. For exampl

Getting Started44MessagesThe HP 10bII+ displays messages about the status of the calculator or informs you that you have attempted an incorrect operat

Business Percentages453 Business PercentagesThe Business Percentage KeysWhen entering data for business percentage calculations, results are calculate

Business Percentages46Example 2You borrow 1,250 from a relative, and you agree to repay the loan in a year with 7% simple interest. How much money wil

Business Percentages47Margin and Markup CalculationsThe 10bII+ can calculate cost, selling price, margin, or markup.To see any value used by the margi

Business Percentages48Using Margin and Markup TogetherExampleA food cooperative buys cases of canned soup with an invoice cost of 9.60 per case. If th

Number Storage and Storage Register Arithmetic494 Number Storage and Storage Register ArithmeticUsing Stored Numbers in CalculationsYou can store numb

Number Storage and Storage Register Arithmetic50Example 2Calculate 10 + 10%, 11 + 10%, and 25 + 10%.Example 3Calculate 23 and 43.Table 4-2 Storing ‘+

Number Storage and Storage Register Arithmetic51Example 4Calculate the percent change between 55 and 32 and store it as a constant. Then calculate the

2Arithmetic with One-and Two-number Functions... 39Last Answer ...

Number Storage and Storage Register Arithmetic52ExampleUse the M register to add 17, 14.25, and 16.95. Then subtract 4.65 and recall the result.Using

Number Storage and Storage Register Arithmetic53With the exception of the statistics registers, you can also use \w and v for application registers. F

Number Storage and Storage Register Arithmetic54Example 1Store 45.7 in R3, multiply by 2.5, and store the result in R3.Example 2Store 1.25 into regist

Picturing Financial Problems555 Picturing Financial ProblemsHow to approach a Financial ProblemThe financial vocabulary of the HP 10bII+ is simplified

Picturing Financial Problems56Signs of Cash FlowsIn cash flow diagrams, money invested is shown as negative and money withdrawn is shown as positive.

Picturing Financial Problems57Compound InterestA compound-interest contract is like a series of simple-interest contracts that are connected. The leng

Picturing Financial Problems58• As a periodic rate. This is the rate that is applied to your money from period to period.• As an annual nominal rate.

Picturing Financial Problems59Figure 4 Cash flow diagram (Borrower’s perspective)One of the values for PV, PMT, FV can be zero. For example, following

Picturing Financial Problems60The following is a cash flow diagram for an investment in a mutual fund. This is an example of a problem that is solved

Time Value of Money Calculations616 Time Value of Money CalculationsUsing the TVM ApplicationThe time value of money (TVM) application is used for com

38 Cash Flow Calculations... 87How to Use the Cash F

Time Value of Money Calculations62To verify values, press vÙ, vÒ, vÏ, vÌ, and vÉ. Pressing v\Ú recalls the total number of payments in years and v\Í s

Time Value of Money Calculations63Figure 7 Cash flow diagram (Calculate PMT)Set to End mode. Press \¯ if BEGIN annunciator is displayed.Part 2At a pri

Time Value of Money Calculations64Part 3If interest is 10.5%, what is the maximum you can spend on the car to lower your car payment to 375.00?Example

Time Value of Money Calculations65Set to End mode. Press \¯ if BEGIN annunciator is displayed.Example: A Mortgage With a Balloon PaymentYou’ve obtaine

Time Value of Money Calculations66Figure 9 Cash flow diagram (Calculate PMT)Set to End mode. Press \¯ if BEGIN annunciator is displayed.Step 2Since th

Time Value of Money Calculations67Figure 10 Cash flow diagram (Calculate FV)The value in PMT should always be rounded to two decimal places when calcu

Time Value of Money Calculations68Figure 11 Cash flow diagram (Calculate the number of years)Since this account has no regular payments (PMT = 0), the

Time Value of Money Calculations69Example: An Individual Retirement AccountYou opened an individual retirement account on April 14, 1995, with a depos

Time Value of Money Calculations70Example: An Annuity AccountYou opt for an early retirement after a successful business career. You have accumulated

Time Value of Money Calculations71Lease CalculationsA lease is a loan of valuable property (like real estate, automobiles, or equipment) for a specifi

4Inverse of Student’s t Probability Lower Tail... 132Conversions from Lower Tail ...

Time Value of Money Calculations72Notice that even if the customer chooses not to buy the car, the lessor still includes a cash flow coming in at the

Time Value of Money Calculations73This solution requires four steps:1. Calculate the present value of the 47 monthly payments: (4 × 12) - 1 = 47.2. Ad

Time Value of Money Calculations74Step 4Add the results of ’Step 2’ and ’Step 3’.AmortizationAmortization is the process of dividing a payment into th

Time Value of Money Calculations75The AMORT key on the HP 10bII+ allows you to calculate.• The amount applied to interest in a range of payments.• The

Time Value of Money Calculations76If you store, recall, or perform any other calculations during amortization, pressing 4 will no longer cycle through

Time Value of Money Calculations77The amount paid toward interest and principal (13,894.67 + 1,579.84 = 15,474.51) equals the total of 12 monthly paym

Time Value of Money Calculations78Amortize the 1st, 25th, and 54th paymentsÌ -310.42 Calculates the monthly payment.Table 6-22 Calculating the amountK

Time Value of Money Calculations79Interest Rate ConversionsThe Interest Conversion application uses three keys: \Ó, \Ð, and \Í. They convert between n

Time Value of Money Calculations80Second BankThird BankFirst Bank offers a slightly better deal since 6.87 is greater than 6.86 and 6.85.Compounding a

Time Value of Money Calculations81Example: Monthly Payments, Daily CompoundingStarting today, you make monthly deposits of 25 to an account paying 5%

At a Glance...11 At a Glance...This section is designed for you if you’re already familiar with calculator operation or financial concepts. You can us

Time Value of Money Calculations82Resetting the TVM KeysPress ]OJ to clear the TVM registers. This sets N, I/YR, PV, PMT, and FV to zero and briefly d

Depreciation837DepreciationOn the 10bII+, depreciation calculations are performed using the functions printed in blue on the keyboard located under th

Depreciation84To perform a depreciation calculation: 1. Enter the original cost of the asset, using Ï.2. Enter the salvage value of the asset, using F

Depreciation85Example 2A machine was purchased for 4,000 and is to be depreciated over four years with a 1,000 salvage value. Using the sum-of-the-yea

Depreciation86Example 3A machine was purchased for 5,000 and is to be depreciated over seven years with no salvage value. Using the double declining b

Cash Flow Calculations878 Cash Flow CalculationsHow to Use the Cash Flow ApplicationThe cash flow application is used to solve problems where cash flo

Cash Flow Calculations88Clearing the Cash Flow MemoryIt is always a good idea to clear the cash flow memory before beginning. To clear cash flows, use

Cash Flow Calculations89Figure 1As illustrated in Figure 1, if no more than 15 data points are stored in the statistics memory, you may store up to 45

Cash Flow Calculations90Calculating Internal Rate of Return1. P r e s s ]O:, and store the desired number of periods per year in P/YR.2. Enter the c

Cash Flow Calculations91NPV and IRR/YR: Discounting Cash FlowsChapter 5 titled, Picturing Financial Problems demonstrates the use of cash flow diagram