FV= ? YR = 6.3%, Yr =, PMT = PV = -2,000.00

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/P 6.00

3,035.28

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Example: An Individual Retirement Account. <RXRSHQHGDQ LQGLYLGXDOUHWLUHPHQWDFFRXQWRQ$SULOZLWKDGHSRVLWRI LVGHGXFWHGIURP\RXUSD\FKHFNDQG\RXDUHSDLGWZLFHDPRQWK 7KHDFFRXQWSD\VDQQXDOLQWHUHVWFRPSRXQGHGVHPLPRQWKO\+RZ PXFKZLOOEHLQWKHDFFRXQWRQ$SULO"

FV= ?

				I/YR = 6.3%
				N = 360 (15 years 24 half-months)
				P/YR = 24
(Half-months periods)					. . .
					. . .
1	2	3	4			360

PMT = -80.00

PV = -2,000.00

6HWWR(QGPRGH3UHVV*OLIBEGINDQQXQFLDWRULVGLVSOD\HG

5: Time Value of Money Calculations 61

Page 61

Image 61

HP F1902-90001 manual FV= ? YR = 6.3%, Yr =, PMT = PV = -2,000.00

Contents

Edition HP part number F1902-90001 Hp 10BII financial calculator Edition May Hewlett-Packard Quality Welcome to the HP 10BIIZRUOGZLGHVHUYLFH FDOFXODWRU $ODUJHFKDUDFWHUGLVSOD\ FeaturesVFKHGXOHV FDOFXODWLRQV Contents 33 3HUFHQW.H\ 54 &OHDULQJ790 53 8VLQJWKH790$SSOLFDWLRQ73 &RPSRXQGLQJDQG3D\PHQW3HULRGV’LIIHU 84 $XWRPDWLF6WRUDJHRI,555DQG139 123 &RQVXPHU7UDQVDFWLRQVLQWKH8QLWHG.LQJGRP 101 $QQXDO3HUFHQWDJH5DWHIRUD/RDQLWKHHV 130 +DOWLQJDQG5HVWDUWLQJ,555 129 ,555&DOFXODWLRQVQWHULQJD*XHVVIRU,555 132 7LPH9DOXHRI0RQH\790Page Basics-At a Glance At a GlanceFRQFHSWVSUHVHQWHGLQWKLVVHFWLRQ 7XUQVFDOFXODWRURQ 7D 3HUFHQW Percentages-At a GlanceRVW 3ULFH $GGWR 6WRUHVDFRQVWDQWRSHUDWLRQ Memory Keys-At a Glance…6WRUHV·ïµDVD OHDUVGLVSOD\ 3D\PHQW Time Value of Money TVM-At a Glance…1XPEHURISD\PHQWVSHU\HDUPRGH 6HWVSD\PHQWVSHU\HDU DOFXODWHVDPRXQW\RX TVM What if…-At a Glance…FDQERUURZ +RZPXFKFDQ\RXERUURZDWDLQWHUHVWUDWH DQGBALDQQXQFLDWRUVUHVSHFWLYHO\ Amortization-At a Glance…’LVSOD\VSULQFLSDO ’LVSOD\VEDODQFH WKHQVROYHIRUWKHXQNQRZQUDWH Interest Rate Conversion-At a Glance…3HULRGVSHU\HDU FRPSRXQGHGPRQWKO\ 1HWSUHVHQWYDOXH IRR/YR and NPV-At a Glance…QWHUVQXPEHURIFRQVHF QWHUV ,5 OHDUVWDWLVWLFDOUHJLVWHUV Statistics-At a Glance… 55.68 10.00 27.50 420.00 Key memory Backspace Accumulate statistical data Cash flows Keyboard MapPage Adjusting the Display Contrast Power On and OffGetting Started Simple Arithmetic Calculations DOFXODWHVUHVXOW KDQJHVWKHVLJQRI Cursor Understanding the Display and KeyboardClearing the Calculator Clearing Memory 26 1 Getting Started Annunciators Statistics Key Shift KeyEHHQSHUIRUPHG DJDLQ Input Key Math FunctionsSwap Key $GGVDQG QWHUV QXPEHU Display Format of NumbersDOFXODWHVWKHSHUFHQW FKDQJH Scientific Notation Specifying Displayed Decimal PlacesDIWHUWKHGHFLPDOSRLQW SODFHV Interchanging the Period and Comma Displaying the Full Precision of NumbersGHFLPDOSRLQWLVQRWVKRZQ ’LYLGHV Rounding Numbers Messages Percent Key Business PercentagesFinding a Percent Percent Change Adding or Subtracting a Percent Margin Calculations Margin and Markup CalculationsMarkup on Cost Calculations GLVSOD\HG 6WRUHVPDUNXS Using Margin and Markup TogetherDOFXODWHVWKHSULFHRQ FDVHRIVRXS Using Constants Using Stored Numbers in CalculationsNumber Storage and Arithmetic RSHUDWLRQV VWDQW FRQVWDQW UHJLVWHU Using the M Register5HFDOOVFRQWHQWVRIWKH UHJLVWHU IROORZLQJ Using Numbered Registers5HFDOOV5 RPSOHWHVILUVW 0XOWLSOLHVLQ5 E\ Doing Arithmetic Inside RegistersDQGVWRUHVUHVXOW LQ5 Doing Arithmetic Using Parentheses in Calculations Power OperatorFDOFXODWH ⋅ DOFXODWHV DOFXODWHV†0XOWLSOLHVWKHUHVXOWE\ 1RFDOFXODWLRQ\HW How to approach a Financial Problem Picturing Financial ProblemsPicturing Financial Problems WRVROYLQJDILQDQFLDOSUREOHP Signs of Cash Flows 46 4 Picturing Financial ProblemsDERXWWKHWUDQVDFWLRQ 000.00 Simple and Compound Interest Periods and Cash FlowsSimple Interest NQRZQEHIRUH\RXFDQEHJLQFDOFXODWLQJ Compound Interest 48 4 Picturing Financial ProblemsDUHEDVHGRQFRPSRXQGLQWHUHVW 005.00 010.03 015.08 020.16 025.26 Recognizing a TVM Problem Two Types of Financial ProblemsInterest Rates = 360 30 PV = 150,000.00357 358 359 PMT = -1,041.40 FV = -10,000.00 000.00 Recognizing a Cash Flow ProblemPage Time Value of Money Calculations Using the TVM Application7RXVH790VHYHUDOSUHUHTXLVLWHVPXVWEHPHW 3D\PHQWVPXVWRFFXUDWUHJXODULQWHUYDOV DOFXODWHVDQDPRUWLDWLRQWDEOH Clearing TVMRFFXUVDWWKHEHJLQQLQJRIWKHILUVWSHULRG RFFXUDWWKHEHJLQQLQJRUHQGRIHDFKSHULRG Loan Calculations Begin and End Modes ERUURZHG 6WRUHVDPRXQW6WRUHVWKHDPRXQWOHIW WRSD\DIWHU\HDUV SXUFKDVHSULFH PV = ? YR = 7.5% = 30 356 357 358 359 360 PMT = End Mode6HWVSHULRGVSHU\HDU 6WRUHVLQWHUHVWUDWH 6WRUHVORDQEDODQFH 6ROYHWKLVSUREOHPXVLQJWZRVWHSVDIWHU\HDUV 6WRUHVRULJLQDOORDQ PV = 172,500.00 YR = 8.8% = 4 WKHQVWRUHV OHDUVDOOUHJLVWHUV Savings CalculationsILUVWGHSRVLW WRDFFXPXODWH YR = FV= ? YR = 6.3%PMT = PV = -2,000.00 SHU\HDU FV = YR = 7% = 600 50 PV = -400,000.00 Begin Mode6WRUHVQXPEHURI GHSRVLWV ZLWKGUDZDOV Lease CalculationsWZRFRPPRQOHDVHFDOFXODWLRQV WKHEHJLQQLQJRIHDFK \LHOG FV = 7,500.00 PMT = ? YR = 10% PV = -13,500.00 Begin ModeYDOXH LQPRQWKV 7KLVVROXWLRQUHTXLUHVIRXUVWHSV Begin Mode PV = ?PMT = -2,400.00 48th payment due up front FV = -15,000.00 DOFXODWHVSUHVHQW SD\PHQWVYDOXHRIPRQWKO\ $GGVDGGLWLRQDO Payment $ AmortizationPrincipal $ Interest $ Time DQGEDODQFH WKHVDPHYDOXHVDJDLQ\WKHVWDUWLQJDQGHQGLQJSD\PHQWVWKDWZLOOEHDPRUWLHG 68 5 Time Value of Money Calculations 13,894.66’LVSOD\VWKH,17 579.82’LVSOD\VWKH35,1178,420.18’LVSOD\VWKH%$/ HQGLQJSHULRGV ’LVSOD\V35,1DQGWKH $PRUWLHWKHVHFRQG\HDU6HWVSD\PHQWVSHU\HDU 70 5 Time Value of Money Calculations ’LVSOD\V,17DQGWKHLQWHU HVW SULQFLSDOSD\PHQW Investments With Different Compounding Periods Interest Rate ConversionsSHULRGGLIIHU IDYRUDEOHLQWHUHVWUDWH 6WRUHVQRPLQDOUDWH 6WRUHVTXDUWHUO\ FRPSRXQGLQJSHULRGV Compounding and Payment Periods Differ6WRUHVQRPLQDOUDWH 6WRUHVPRQWKO\FRP SRXQGLQJSHULRGV 6WRUHVQRPLQDOUDWH 6WRUHVSD\PHQW Step . &DOFXODWHWKHIXWXUHYD XH6WRUHVWRWDOQXPEHURI DOFXODWHVEDODQFHDIWHU Cash Flow Calculations How to Use the Cash Flow ApplicationWKH+3%,, QWHUWKHQXPEHURISHULRGVSHU\HDU QWHUVILQDOFDVKIORZ QWHUVQHWFDVKIORZQRPLQDO\LHOG 0RQWKO\\LHOG Organizing Cash Flows NPV and IRR/YR Discontinuing Cash Flows IORZVXVLQJWKHIROORZLQJVWHSV Entering Cash FlowsEHHQHQWHUHG 3UHVV*&WRFOHDUWKHUHVLVWHUV JURXSDPRXQW QWHUVQXPEHURI UHSHWLWLRQV Viewing and Replacing Cash FlowsIORZJURXSDPRXQW QWHUVQXPEHURI UHSHWLWLRQV 7RYLHZDFDVKIORZSUHVV 7RUHSODFHDFDVKIORZDPRXQWSUHVV Calculating Net Present Value7KHVHVWHSVGHVFULEHKRZWRFDOFXODWH139 QWHUVQXPEHURI RFFXUUHQFHV OHDUVUHJLVWHUVYR = 15% 10,000 500 82 6 Cash Flow Calculations FDOFXODWHWKHQHWSUHVHQWYDOXH 3UHVV*9 Calculating Internal Rate of ReturnSUHYLRXVHDPSOH 000 10,000 500 28,000 11 13 15 17 IRR/YR = ? 19 21 23 84 6 Cash Flow Calculations Automatic Storage of IRR/YR and NPV Clearing Statistical Data Statistical CalculationsHLJKWHGPHDQ Statistical Calculations Entering Statistical Data Two-Variable Statistics and Weighted MeanOne-Variable Statistics VWDWLVWLFDOUHJLVWHUV Summary of Statistical Calculations Correcting Statistical DataCorrecting One-Variable Data Correcting Two-Variable Data 6XPRIWKHYDOXHV LI\RXHQWHUHG\GDWD6XPRIWKH\YDOXHV 88 7 Statistical Calculations DOFXODWHVWKHURRWPHDQ VTXDUH 82.75 ’LVSOD\VPHDQRIZHLJKWV\ Linear Regression and EstimationIROORZV 90 7 Statistical Calculations FRHIILFLHQW ’LVSOD\VVORSHPLQXWHVRIDGYHUWLVLQJ 357.38VWLPDWHVVDOHVLI 783.25VWLPDWHVVDOHVLI Weighted Mean Page Additional Examples Setting a Sales PriceBusiness Applications SURGXFW VHYHQ Forecasting Based on HistoryVWLPDWHVVDOHVIRU\HDU OHDUVVWDWLVWLFVUHJLVWHUV Cost of Not Taking a Cash Discount Simple Annual Interest Loans and MortgagesContinuous Compounding 17567 Yield of a Discounted or Premium Mortgage QWHUVDPRXQWOHIWWRSD\ PRUWJDJHDIWHU\HDUV DOFXODWHVUHJXODU Annual Percentage Rate for a Loan With Fees FRQVLGHULQJIHHV 72&DOFXODWHV$35LQWHUHVWD HPDGH GXH Loan With a Partial Odd First Period DPRXQW Automobile LoanGHDOHULVRIIHULQJWZRFKRLFHVIRUILQDQFLQJ UHEDWH LWKZKLFKFKRLFHGR\RXSD\OHVVIRUWKHFDU Canadian Mortgages IROORZV What if … TVM Calculations106 8 Additional Examples WRSD\RIIORDQ LQWHUHVWSDLGRQWKHFRQWUDFWELZHHNO\SD\PHQWV 6WRUHVQHZWHUP Saving for College Costs Savings$15,000 YR = 9% Year FV from 6WRUHVDQQXDO ZLWKGUDZDO 6WRUHVQXPEHURI ZLWKGUDZDOVPrevious 142 143 144 PMT = ? QHHG Gains That Go Untaxed Until WithdrawalVWDUWLQJZLWK 110 8 Additional Examples UHWLUHPHQW VWDUWZLWK 6WRUHVDPRXQWRI DQQXDOSD\PHQWRILQWHUHVW LQIODWLRQUDWH VWDUWLQJZLWK 6WRUHVDPRXQWRI DQQXDOSD\PHQW Value of a Taxable Retirement Account6WRUHVDPRXQW\RXDUH DFFRXQWDWUHWLUHPHQW Wrap-Around Mortgages Cash Flow Examples QWHUVQHWSD\PHQWIRU KHQ\RXJURXSWKHDERYHFDVKIORZV\RXOOILQGWKDWQHWPRQWKV WLPHVSD\PHQWRFFXUV FXUUHQWEDODQFHRIWKHDFFRXQW Net Future ValueJURXS JURXS 116 8 Additional Examples YDOXH139 Assistance, Batteries, and Service Assistance, Batteries, and ServiceAnswers to Common Questions 3UHVV*SDJH KDWGRHVDQ·µLQDQXPEHUIRUHDPSOH†PHDQ Environmental LimitsKDWGRHVPENDLQWKHGLVSOD\PHDQ 6WRUDJHWHPSHUDWXUH†ƒWRƒ&†ƒWRƒ Low Power Annunciator Power and BatteriesBattery Specifications Installing Batteries VHFWLRQ 5HPRYHERWKEDWWHULHV QVWDOOQHZEDWWHULHV Determining if the Calculator Requires Service HUDVHWKHPHPRU\VHHEHORZ FDVHWKHFDOFXODWRUUHTXLUHVDVHUYLFH What Is Covered Limited One-Year WarrantyWhat Is Not Covered EDWWHU\DQGEDWWHU\OHDNDJHZDUUDQWLHV Obtaining Service If the Calculator Requires ServiceConsumer Transactions in the United Kingdom XSGDWHSURGXFWVRQFHVROG Warranty on Service Service ChargeShipping Instructions Regulatory Information Service AgreementsRSHUDWHWKLVHTXLSPHQW End-user terms and conditions Assistance, Batteries, and Service Page IRR/YR Calculations More About CalculationsPossible Outcomes of Calculating IRR/YR KHOS\RXLQWHUSUHWZKDWKDVKDSSHQHG Tering a Guess for IRR/YR Halting and Restarting IRR/YRRQHQHJDWLYHFDVKIORZ $IWHU\RXYHLQWHUUXSWHGWKHFDOFXODWLRQ Range of Numbers Effect of Using Σ- to Correct DataIROORZLQJWKLVDSSHQGL WRFOHDUWKHVWDWLVWLFDOUHJLVWHUVDQGUHHQWHUWKHGDWD Margin and Markup Calculations EquationsTime Value of Money TVM Amortization RUHDFKSD\PHQWDPRUWLHG Interest Rate Conversions  Cash-Flow CalculationsWKHJURXSQXPEHURIWKHODVWJURXSRIFDVKIORZV Σx = StatisticsPage 0HPRU\KDVEHHQHUDVHGSDJH MessagesRS\ULJKWPHVVDJH FRQGLWLRQ Uflo 5XQQLQJ$FDOFXODWLRQLVLQSURFHVV Special Keys Index Gldjudpv Glvfrxqw Hqwhulqj Htxdwlrqv HJLQPRGH RUURZLQJHTXLW\ \RXWYDOXH Uhsodflqj Xqhyhq Ylhzlqj KDLQFDOFXODWLRQV LQHDUUHJUHVVLRQ , Uhvwduwlqj Rjdulwkp Zhljkwhg , 0HPRU\ 3HUFHQW DWDJODQFH 5DWH Hiihfwlyh , DULWKPHWLFLQ Qxpehuhg Hvwlpdwlrq 6LJQFKDQJLQJ Uhjlvwhuv Vxppdwlrq

3,035.28

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FV= ?

I/YR = 6.3%

P/YR = 24

PMT = -80.00

PV = -2,000.00

5: Time Value of Money Calculations 61

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