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56 5: Time Value of Money Calculations

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Contents

Hp 10BII financial calculator Edition HP part number F1902-90001 Edition May Welcome to the HP 10BII Hewlett-Packard QualityZRUOGZLGHVHUYLFH FDOFXODWRU Features $ODUJHFKDUDFWHUGLVSOD\VFKHGXOHV FDOFXODWLRQV Contents 33 3HUFHQW.H\ 53 8VLQJWKH790$SSOLFDWLRQ 54 &OHDULQJ79073 &RPSRXQGLQJDQG3D\PHQW3HULRGV’LIIHU 84 $XWRPDWLF6WRUDJHRI,555DQG139 101 $QQXDO3HUFHQWDJH5DWHIRUD/RDQLWKHHV 123 &RQVXPHU7UDQVDFWLRQVLQWKH8QLWHG.LQJGRP 129 ,555&DOFXODWLRQV 130 +DOWLQJDQG5HVWDUWLQJ,555QWHULQJD*XHVVIRU,555 132 7LPH9DOXHRI0RQH\790Page At a Glance Basics-At a GlanceFRQFHSWVSUHVHQWHGLQWKLVVHFWLRQ 7XUQVFDOFXODWRURQ Percentages-At a Glance 7D 3HUFHQWRVW 3ULFH $GGWR Memory Keys-At a Glance… 6WRUHVDFRQVWDQWRSHUDWLRQ6WRUHV·ïµDVD OHDUVGLVSOD\ Time Value of Money TVM-At a Glance… 3D\PHQW1XPEHURISD\PHQWVSHU\HDUPRGH 6HWVSD\PHQWVSHU\HDU TVM What if…-At a Glance… DOFXODWHVDPRXQW\RXFDQERUURZ +RZPXFKFDQ\RXERUURZDWDLQWHUHVWUDWH Amortization-At a Glance… DQGBALDQQXQFLDWRUVUHVSHFWLYHO\’LVSOD\VSULQFLSDO ’LVSOD\VEDODQFH Interest Rate Conversion-At a Glance… WKHQVROYHIRUWKHXQNQRZQUDWH3HULRGVSHU\HDU FRPSRXQGHGPRQWKO\ IRR/YR and NPV-At a Glance… 1HWSUHVHQWYDOXHQWHUVQXPEHURIFRQVHF 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 Power On and Off Adjusting the Display ContrastGetting Started Simple Arithmetic Calculations KDQJHVWKHVLJQRI DOFXODWHVUHVXOW Understanding the Display and Keyboard CursorClearing the Calculator Clearing Memory Annunciators 26 1 Getting Started Shift Key Statistics KeyEHHQSHUIRUPHG DJDLQ Math Functions Input KeySwap Key $GGVDQG Display Format of Numbers QWHUV QXPEHUDOFXODWHVWKHSHUFHQW FKDQJH Specifying Displayed Decimal Places Scientific NotationDIWHUWKHGHFLPDOSRLQW SODFHV Displaying the Full Precision of Numbers Interchanging the Period and CommaGHFLPDOSRLQWLVQRWVKRZQ ’LYLGHV Messages Rounding Numbers Finding a Percent Business PercentagesPercent Key Adding or Subtracting a Percent Percent Change Margin and Markup Calculations Margin CalculationsMarkup on Cost Calculations GLVSOD\HG Using Margin and Markup Together 6WRUHVPDUNXSDOFXODWHVWKHSULFHRQ FDVHRIVRXS Using Stored Numbers in Calculations Using ConstantsNumber Storage and Arithmetic RSHUDWLRQV FRQVWDQW VWDQW Using the M Register UHJLVWHU5HFDOOVFRQWHQWVRIWKH UHJLVWHU Using Numbered Registers IROORZLQJ5HFDOOV5 RPSOHWHVILUVW Doing Arithmetic Inside Registers 0XOWLSOLHVLQ5 E\DQGVWRUHVUHVXOW LQ5 Doing Arithmetic Power Operator Using Parentheses in CalculationsFDOFXODWH ⋅ DOFXODWHV† DOFXODWHV 0XOWLSOLHVWKHUHVXOWE\ 1RFDOFXODWLRQ\HW Picturing Financial Problems How to approach a Financial ProblemPicturing Financial Problems WRVROYLQJDILQDQFLDOSUREOHP 46 4 Picturing Financial Problems Signs of Cash FlowsDERXWWKHWUDQVDFWLRQ 000.00 Periods and Cash Flows Simple and Compound InterestSimple Interest NQRZQEHIRUH\RXFDQEHJLQFDOFXODWLQJ 48 4 Picturing Financial Problems Compound InterestDUHEDVHGRQFRPSRXQGLQWHUHVW 005.00 010.03 015.08 020.16 025.26 Interest Rates Two Types of Financial ProblemsRecognizing a TVM Problem PV = 150,000.00 = 360 30357 358 359 PMT = -1,041.40 FV = -10,000.00 Recognizing a Cash Flow Problem 000.00Page Using the TVM Application Time Value of Money Calculations7RXVH790VHYHUDOSUHUHTXLVLWHVPXVWEHPHW 3D\PHQWVPXVWRFFXUDWUHJXODULQWHUYDOV Clearing TVM DOFXODWHVDQDPRUWLDWLRQWDEOHRFFXUVDWWKHEHJLQQLQJRIWKHILUVWSHULRG RFFXUDWWKHEHJLQQLQJRUHQGRIHDFKSHULRG Begin and End Modes Loan Calculations 6WRUHVDPRXQW ERUURZHG6WRUHVWKHDPRXQWOHIW WRSD\DIWHU\HDUV PV = ? YR = 7.5% = 30 356 357 358 359 360 PMT = End Mode SXUFKDVHSULFH6HWVSHULRGVSHU\HDU 6WRUHVLQWHUHVWUDWH 6ROYHWKLVSUREOHPXVLQJWZRVWHSV 6WRUHVORDQEDODQFHDIWHU\HDUV 6WRUHVRULJLQDOORDQ WKHQVWRUHV PV = 172,500.00 YR = 8.8% = 4 Savings Calculations OHDUVDOOUHJLVWHUVILUVWGHSRVLW WRDFFXPXODWH PMT = PV = -2,000.00 FV= ? YR = 6.3%YR = FV = YR = 7% = 600 50 PV = -400,000.00 Begin Mode SHU\HDU6WRUHVQXPEHURI GHSRVLWV Lease Calculations ZLWKGUDZDOVWZRFRPPRQOHDVHFDOFXODWLRQV WKHEHJLQQLQJRIHDFK FV = 7,500.00 PMT = ? YR = 10% PV = -13,500.00 Begin Mode \LHOGYDOXH LQPRQWKV PMT = -2,400.00 48th payment due up front FV = -15,000.00 Begin Mode PV = ?7KLVVROXWLRQUHTXLUHVIRXUVWHSV SD\PHQWV DOFXODWHVSUHVHQWYDOXHRIPRQWKO\ $GGVDGGLWLRQDO Principal $ Interest $ Time AmortizationPayment $ WKHVDPHYDOXHVDJDLQ DQGEDODQFH\WKHVWDUWLQJDQGHQGLQJSD\PHQWVWKDWZLOOEHDPRUWLHG 68 5 Time Value of Money Calculations 579.82’LVSOD\VWKH35,1 13,894.66’LVSOD\VWKH,17178,420.18’LVSOD\VWKH%$/ HQGLQJSHULRGV $PRUWLHWKHVHFRQG\HDU ’LVSOD\V35,1DQGWKH6HWVSD\PHQWVSHU\HDU 70 5 Time Value of Money Calculations SULQFLSDOSD\PHQW ’LVSOD\V,17DQGWKHLQWHU HVW Interest Rate Conversions Investments With Different Compounding PeriodsSHULRGGLIIHU IDYRUDEOHLQWHUHVWUDWH Compounding and Payment Periods Differ 6WRUHVQRPLQDOUDWH 6WRUHVTXDUWHUO\ FRPSRXQGLQJSHULRGV6WRUHVQRPLQDOUDWH 6WRUHVPRQWKO\FRP SRXQGLQJSHULRGV 6WRUHVQRPLQDOUDWH Step . &DOFXODWHWKHIXWXUHYD XH 6WRUHVSD\PHQW6WRUHVWRWDOQXPEHURI DOFXODWHVEDODQFHDIWHU How to Use the Cash Flow Application Cash Flow CalculationsWKH+3%,, QWHUWKHQXPEHURISHULRGVSHU\HDU QWHUVQHWFDVKIORZ QWHUVILQDOFDVKIORZQRPLQDO\LHOG 0RQWKO\\LHOG NPV and IRR/YR Discontinuing Cash Flows Organizing Cash Flows Entering Cash Flows IORZVXVLQJWKHIROORZLQJVWHSVEHHQHQWHUHG 3UHVV*&WRFOHDUWKHUHVLVWHUV Viewing and Replacing Cash Flows JURXSDPRXQW QWHUVQXPEHURI UHSHWLWLRQVIORZJURXSDPRXQW QWHUVQXPEHURI UHSHWLWLRQV 7RYLHZDFDVKIORZSUHVV Calculating Net Present Value 7RUHSODFHDFDVKIORZDPRXQWSUHVV7KHVHVWHSVGHVFULEHKRZWRFDOFXODWH139 YR = 15% 10,000 500 OHDUVUHJLVWHUVQWHUVQXPEHURI RFFXUUHQFHV FDOFXODWHWKHQHWSUHVHQWYDOXH 82 6 Cash Flow Calculations Calculating Internal Rate of Return 3UHVV*9SUHYLRXVHDPSOH 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 Statistical Calculations Clearing Statistical DataHLJKWHGPHDQ Statistical Calculations Two-Variable Statistics and Weighted Mean Entering Statistical DataOne-Variable Statistics VWDWLVWLFDOUHJLVWHUV Correcting Statistical Data Summary of Statistical CalculationsCorrecting One-Variable Data Correcting Two-Variable Data LI\RXHQWHUHG\GDWD 6XPRIWKHYDOXHV6XPRIWKH\YDOXHV 88 7 Statistical Calculations VTXDUH DOFXODWHVWKHURRWPHDQ Linear Regression and Estimation 82.75 ’LVSOD\VPHDQRIZHLJKWV\IROORZV 90 7 Statistical Calculations ’LVSOD\VVORSH FRHIILFLHQWPLQXWHVRIDGYHUWLVLQJ 357.38VWLPDWHVVDOHVLI 783.25VWLPDWHVVDOHVLI Weighted Mean Page Setting a Sales Price Additional ExamplesBusiness Applications SURGXFW Forecasting Based on History VHYHQVWLPDWHVVDOHVIRU\HDU OHDUVVWDWLVWLFVUHJLVWHUV Cost of Not Taking a Cash Discount Loans and Mortgages Simple Annual InterestContinuous Compounding 17567 Yield of a Discounted or Premium Mortgage PRUWJDJH QWHUVDPRXQWOHIWWRSD\DIWHU\HDUV DOFXODWHVUHJXODU Annual Percentage Rate for a Loan With Fees 72&DOFXODWHV$35 FRQVLGHULQJIHHVLQWHUHVWD HPDGH GXH Loan With a Partial Odd First Period Automobile Loan DPRXQWGHDOHULVRIIHULQJWZRFKRLFHVIRUILQDQFLQJ UHEDWH LWKZKLFKFKRLFHGR\RXSD\OHVVIRUWKHFDU Canadian Mortgages 106 8 Additional Examples What if … TVM CalculationsIROORZV LQWHUHVWSDLGRQWKHFRQWUDFW WRSD\RIIORDQELZHHNO\SD\PHQWV 6WRUHVQHZWHUP Savings Saving for College Costs$15,000 YR = 9% Year 6WRUHVDQQXDO ZLWKGUDZDO 6WRUHVQXPEHURI ZLWKGUDZDOV FV fromPrevious 142 143 144 PMT = ? Gains That Go Untaxed Until Withdrawal QHHGVWDUWLQJZLWK 110 8 Additional Examples VWDUWZLWK 6WRUHVDPRXQWRI DQQXDOSD\PHQW UHWLUHPHQWRILQWHUHVW LQIODWLRQUDWH Value of a Taxable Retirement Account VWDUWLQJZLWK 6WRUHVDPRXQWRI DQQXDOSD\PHQW6WRUHVDPRXQW\RXDUH DFFRXQWDWUHWLUHPHQW Cash Flow Examples Wrap-Around Mortgages KHQ\RXJURXSWKHDERYHFDVKIORZV\RXOOILQGWKDW QWHUVQHWSD\PHQWIRUQHWPRQWKV WLPHVSD\PHQWRFFXUV Net Future Value FXUUHQWEDODQFHRIWKHDFFRXQWJURXS JURXS YDOXH139 116 8 Additional Examples Assistance, Batteries, and Service Assistance, Batteries, and ServiceAnswers to Common Questions 3UHVV*SDJH Environmental Limits KDWGRHVDQ·µLQDQXPEHUIRUHDPSOH†PHDQKDWGRHVPENDLQWKHGLVSOD\PHDQ 6WRUDJHWHPSHUDWXUH†ƒWRƒ&†ƒWRƒ Power and Batteries Low Power AnnunciatorBattery Specifications Installing Batteries 5HPRYHERWKEDWWHULHV VHFWLRQ Determining if the Calculator Requires Service QVWDOOQHZEDWWHULHV HUDVHWKHPHPRU\VHHEHORZ FDVHWKHFDOFXODWRUUHTXLUHVDVHUYLFH Limited One-Year Warranty What Is CoveredWhat Is Not Covered EDWWHU\DQGEDWWHU\OHDNDJHZDUUDQWLHV If the Calculator Requires Service Obtaining ServiceConsumer Transactions in the United Kingdom XSGDWHSURGXFWVRQFHVROG Shipping Instructions Service ChargeWarranty on Service RSHUDWHWKLVHTXLSPHQW Service AgreementsRegulatory Information End-user terms and conditions Assistance, Batteries, and Service Page More About Calculations IRR/YR CalculationsPossible Outcomes of Calculating IRR/YR KHOS\RXLQWHUSUHWZKDWKDVKDSSHQHG Halting and Restarting IRR/YR Tering a Guess for IRR/YRRQHQHJDWLYHFDVKIORZ $IWHU\RXYHLQWHUUXSWHGWKHFDOFXODWLRQ Effect of Using Σ- to Correct Data Range of NumbersIROORZLQJWKLVDSSHQGL WRFOHDUWKHVWDWLVWLFDOUHJLVWHUVDQGUHHQWHUWKHGDWD Equations Margin and Markup CalculationsTime Value of Money TVM Amortization Interest Rate Conversions RUHDFKSD\PHQWDPRUWLHG WKHJURXSQXPEHURIWKHODVWJURXSRIFDVKIORZV Cash-Flow Calculations Statistics Σx =Page Messages 0HPRU\KDVEHHQHUDVHGSDJH RS\ULJKWPHVVDJH FRQGLWLRQ 5XQQLQJ$FDOFXODWLRQLVLQSURFHVV Uflo Index Special Keys HJLQPRGH RUURZLQJHTXLW\ \RXWYDOXH Gldjudpv Glvfrxqw Hqwhulqj Htxdwlrqv Uhsodflqj Xqhyhq Ylhzlqj KDLQFDOFXODWLRQV Uhvwduwlqj LQHDUUHJUHVVLRQ , Rjdulwkp Zhljkwhg , 0HPRU\ DWDJODQFH 3HUFHQW 5DWH Hiihfwlyh , DULWKPHWLFLQ Qxpehuhg 6LJQFKDQJLQJ Hvwlpdwlrq Uhjlvwhuv Vxppdwlrq