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66 5: Time Value of Money Calculations

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Contents

Hp 10BII financial calculator Edition HP part number F1902-90001 Edition May ZRUOGZLGHVHUYLFH Welcome to the HP 10BIIHewlett-Packard Quality FDOFXODWRU VFKHGXOHV Features$ODUJHFKDUDFWHUGLVSOD\ FDOFXODWLRQV Contents 33 3HUFHQW.H\ 73 &RPSRXQGLQJDQG3D\PHQW3HULRGV’LIIHU 53 8VLQJWKH790$SSOLFDWLRQ54 &OHDULQJ790 84 $XWRPDWLF6WRUDJHRI,555DQG139 101 $QQXDO3HUFHQWDJH5DWHIRUD/RDQLWKHHV 123 &RQVXPHU7UDQVDFWLRQVLQWKH8QLWHG.LQJGRP QWHULQJD*XHVVIRU,555 129 ,555&DOFXODWLRQV130 +DOWLQJDQG5HVWDUWLQJ,555 132 7LPH9DOXHRI0RQH\790Page FRQFHSWVSUHVHQWHGLQWKLVVHFWLRQ At a GlanceBasics-At a Glance 7XUQVFDOFXODWRURQ RVW 3ULFH Percentages-At a Glance7D 3HUFHQW $GGWR 6WRUHV·ïµDVD Memory Keys-At a Glance…6WRUHVDFRQVWDQWRSHUDWLRQ OHDUVGLVSOD\ 1XPEHURISD\PHQWVSHU\HDUPRGH Time Value of Money TVM-At a Glance…3D\PHQW 6HWVSD\PHQWVSHU\HDU FDQERUURZ TVM What if…-At a Glance…DOFXODWHVDPRXQW\RX +RZPXFKFDQ\RXERUURZDWDLQWHUHVWUDWH ’LVSOD\VSULQFLSDO Amortization-At a Glance…DQGBALDQQXQFLDWRUVUHVSHFWLYHO\ ’LVSOD\VEDODQFH 3HULRGVSHU\HDU Interest Rate Conversion-At a Glance…WKHQVROYHIRUWKHXQNQRZQUDWH FRPSRXQGHGPRQWKO\ QWHUVQXPEHURIFRQVHF IRR/YR and NPV-At a Glance…1HWSUHVHQWYDOXH QWHUV ,5 Statistics-At a Glance… OHDUVWDWLVWLFDOUHJLVWHUV 55.68 10.00 27.50 420.00 Keyboard Map Key memory Backspace Accumulate statistical data Cash flowsPage Getting Started Power On and OffAdjusting the Display Contrast Simple Arithmetic Calculations KDQJHVWKHVLJQRI DOFXODWHVUHVXOW Clearing the Calculator Understanding the Display and KeyboardCursor Clearing Memory Annunciators 26 1 Getting Started EHHQSHUIRUPHG Shift KeyStatistics Key DJDLQ Swap Key Math FunctionsInput Key $GGVDQG DOFXODWHVWKHSHUFHQW Display Format of NumbersQWHUV QXPEHU FKDQJH DIWHUWKHGHFLPDOSRLQW Specifying Displayed Decimal PlacesScientific Notation SODFHV GHFLPDOSRLQWLVQRWVKRZQ Displaying the Full Precision of NumbersInterchanging the Period and Comma ’LYLGHV Messages Rounding Numbers Business Percentages Percent KeyFinding a Percent Adding or Subtracting a Percent Percent Change Markup on Cost Calculations Margin and Markup CalculationsMargin Calculations GLVSOD\HG DOFXODWHVWKHSULFHRQ Using Margin and Markup Together6WRUHVPDUNXS FDVHRIVRXS Number Storage and Arithmetic Using Stored Numbers in CalculationsUsing Constants RSHUDWLRQV FRQVWDQW VWDQW 5HFDOOVFRQWHQWVRIWKH Using the M RegisterUHJLVWHU UHJLVWHU 5HFDOOV5 Using Numbered RegistersIROORZLQJ RPSOHWHVILUVW DQGVWRUHVUHVXOW Doing Arithmetic Inside Registers0XOWLSOLHVLQ5 E\ LQ5 Doing Arithmetic FDOFXODWH Power OperatorUsing Parentheses in Calculations ⋅ 0XOWLSOLHVWKHUHVXOWE\ DOFXODWHV†DOFXODWHV 1RFDOFXODWLRQ\HW Picturing Financial Problems Picturing Financial ProblemsHow to approach a Financial Problem WRVROYLQJDILQDQFLDOSUREOHP DERXWWKHWUDQVDFWLRQ 46 4 Picturing Financial ProblemsSigns of Cash Flows 000.00 Simple Interest Periods and Cash FlowsSimple and Compound Interest NQRZQEHIRUH\RXFDQEHJLQFDOFXODWLQJ DUHEDVHGRQFRPSRXQGLQWHUHVW 48 4 Picturing Financial ProblemsCompound Interest 005.00 010.03 015.08 020.16 025.26 Two Types of Financial Problems Recognizing a TVM ProblemInterest Rates 357 358 359 PV = 150,000.00= 360 30 PMT = -1,041.40 FV = -10,000.00 Recognizing a Cash Flow Problem 000.00Page 7RXVH790VHYHUDOSUHUHTXLVLWHVPXVWEHPHW Using the TVM ApplicationTime Value of Money Calculations 3D\PHQWVPXVWRFFXUDWUHJXODULQWHUYDOV RFFXUVDWWKHEHJLQQLQJRIWKHILUVWSHULRG Clearing TVMDOFXODWHVDQDPRUWLDWLRQWDEOH RFFXUDWWKHEHJLQQLQJRUHQGRIHDFKSHULRG Begin and End Modes Loan Calculations 6WRUHVWKHDPRXQWOHIW 6WRUHVDPRXQWERUURZHG WRSD\DIWHU\HDUV 6HWVSHULRGVSHU\HDU PV = ? YR = 7.5% = 30 356 357 358 359 360 PMT = End ModeSXUFKDVHSULFH 6WRUHVLQWHUHVWUDWH DIWHU\HDUV 6ROYHWKLVSUREOHPXVLQJWZRVWHSV6WRUHVORDQEDODQFH 6WRUHVRULJLQDOORDQ WKHQVWRUHV PV = 172,500.00 YR = 8.8% = 4 ILUVWGHSRVLW Savings CalculationsOHDUVDOOUHJLVWHUV WRDFFXPXODWH FV= ? YR = 6.3% YR =PMT = PV = -2,000.00 6WRUHVQXPEHURI FV = YR = 7% = 600 50 PV = -400,000.00 Begin ModeSHU\HDU GHSRVLWV WZRFRPPRQOHDVHFDOFXODWLRQV Lease CalculationsZLWKGUDZDOV WKHEHJLQQLQJRIHDFK YDOXH FV = 7,500.00 PMT = ? YR = 10% PV = -13,500.00 Begin Mode\LHOG LQPRQWKV Begin Mode PV = ? 7KLVVROXWLRQUHTXLUHVIRXUVWHSVPMT = -2,400.00 48th payment due up front FV = -15,000.00 YDOXHRIPRQWKO\ SD\PHQWVDOFXODWHVSUHVHQW $GGVDGGLWLRQDO Amortization Payment $Principal $ Interest $ Time \WKHVWDUWLQJDQGHQGLQJSD\PHQWVWKDWZLOOEHDPRUWLHG WKHVDPHYDOXHVDJDLQDQGEDODQFH 68 5 Time Value of Money Calculations 178,420.18’LVSOD\VWKH%$/ 579.82’LVSOD\VWKH35,113,894.66’LVSOD\VWKH,17 HQGLQJSHULRGV 6HWVSD\PHQWVSHU\HDU $PRUWLHWKHVHFRQG\HDU’LVSOD\V35,1DQGWKH 70 5 Time Value of Money Calculations SULQFLSDOSD\PHQW ’LVSOD\V,17DQGWKHLQWHU HVW SHULRGGLIIHU Interest Rate ConversionsInvestments With Different Compounding Periods IDYRUDEOHLQWHUHVWUDWH 6WRUHVQRPLQDOUDWH 6WRUHVPRQWKO\FRP SRXQGLQJSHULRGV Compounding and Payment Periods Differ6WRUHVQRPLQDOUDWH 6WRUHVTXDUWHUO\ FRPSRXQGLQJSHULRGV 6WRUHVQRPLQDOUDWH 6WRUHVWRWDOQXPEHURI Step . &DOFXODWHWKHIXWXUHYD XH6WRUHVSD\PHQW DOFXODWHVEDODQFHDIWHU WKH+3%,, How to Use the Cash Flow ApplicationCash Flow Calculations QWHUWKHQXPEHURISHULRGVSHU\HDU QRPLQDO\LHOG QWHUVQHWFDVKIORZQWHUVILQDOFDVKIORZ 0RQWKO\\LHOG NPV and IRR/YR Discontinuing Cash Flows Organizing Cash Flows EHHQHQWHUHG Entering Cash FlowsIORZVXVLQJWKHIROORZLQJVWHSV 3UHVV*&WRFOHDUWKHUHVLVWHUV IORZJURXSDPRXQW QWHUVQXPEHURI UHSHWLWLRQV Viewing and Replacing Cash FlowsJURXSDPRXQW QWHUVQXPEHURI UHSHWLWLRQV 7RYLHZDFDVKIORZSUHVV 7KHVHVWHSVGHVFULEHKRZWRFDOFXODWH139 Calculating Net Present Value7RUHSODFHDFDVKIORZDPRXQWSUHVV OHDUVUHJLVWHUV QWHUVQXPEHURI RFFXUUHQFHVYR = 15% 10,000 500 FDOFXODWHWKHQHWSUHVHQWYDOXH 82 6 Cash Flow Calculations SUHYLRXVHDPSOH Calculating Internal Rate of Return 3UHVV*9 000 10,000 500 28,000 11 13 15 17 IRR/YR = ? 19 21 23 Automatic Storage of IRR/YR and NPV 84 6 Cash Flow Calculations HLJKWHGPHDQ Statistical CalculationsClearing Statistical Data Statistical Calculations One-Variable Statistics Two-Variable Statistics and Weighted MeanEntering Statistical Data VWDWLVWLFDOUHJLVWHUV Correcting One-Variable Data Correcting Statistical DataSummary of Statistical Calculations Correcting Two-Variable Data 6XPRIWKH\YDOXHV LI\RXHQWHUHG\GDWD6XPRIWKHYDOXHV 88 7 Statistical Calculations VTXDUH DOFXODWHVWKHURRWPHDQ IROORZV Linear Regression and Estimation82.75 ’LVSOD\VPHDQRIZHLJKWV\ 90 7 Statistical Calculations PLQXWHVRIDGYHUWLVLQJ 357.38VWLPDWHVVDOHVLI ’LVSOD\VVORSHFRHIILFLHQW 783.25VWLPDWHVVDOHVLI Weighted Mean Page Business Applications Setting a Sales PriceAdditional Examples SURGXFW VWLPDWHVVDOHVIRU\HDU Forecasting Based on HistoryVHYHQ OHDUVVWDWLVWLFVUHJLVWHUV Cost of Not Taking a Cash Discount Continuous Compounding Loans and MortgagesSimple Annual Interest 17567 Yield of a Discounted or Premium Mortgage DIWHU\HDUV PRUWJDJHQWHUVDPRXQWOHIWWRSD\ DOFXODWHVUHJXODU Annual Percentage Rate for a Loan With Fees LQWHUHVWD HPDGH 72&DOFXODWHV$35FRQVLGHULQJIHHV GXH Loan With a Partial Odd First Period GHDOHULVRIIHULQJWZRFKRLFHVIRUILQDQFLQJ Automobile LoanDPRXQW UHEDWH LWKZKLFKFKRLFHGR\RXSD\OHVVIRUWKHFDU Canadian Mortgages What if … TVM Calculations IROORZV106 8 Additional Examples ELZHHNO\SD\PHQWV LQWHUHVWSDLGRQWKHFRQWUDFWWRSD\RIIORDQ 6WRUHVQHZWHUP $15,000 YR = 9% SavingsSaving for College Costs Year Previous 6WRUHVDQQXDO ZLWKGUDZDO 6WRUHVQXPEHURI ZLWKGUDZDOVFV from 142 143 144 PMT = ? 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