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5: Time Value of Money Calculations 71

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Contents

Edition HP part number F1902-90001 Hp 10BII financial calculator Edition May FDOFXODWRU Welcome to the HP 10BIIHewlett-Packard Quality ZRUOGZLGHVHUYLFH FDOFXODWLRQV Features$ODUJHFKDUDFWHUGLVSOD\ VFKHGXOHV Contents 33 3HUFHQW.H\ 84 $XWRPDWLF6WRUDJHRI,555DQG139 53 8VLQJWKH790$SSOLFDWLRQ54 &OHDULQJ790 73 &RPSRXQGLQJDQG3D\PHQW3HULRGV’LIIHU 123 &RQVXPHU7UDQVDFWLRQVLQWKH8QLWHG.LQJGRP 101 $QQXDO3HUFHQWDJH5DWHIRUD/RDQLWKHHV 132 7LPH9DOXHRI0RQH\790 129 ,555&DOFXODWLRQV130 +DOWLQJDQG5HVWDUWLQJ,555 QWHULQJD*XHVVIRU,555Page 7XUQVFDOFXODWRURQ At a GlanceBasics-At a Glance FRQFHSWVSUHVHQWHGLQWKLVVHFWLRQ $GGWR Percentages-At a Glance7D 3HUFHQW RVW 3ULFH OHDUVGLVSOD\ Memory Keys-At a Glance…6WRUHVDFRQVWDQWRSHUDWLRQ 6WRUHV·ïµDVD 6HWVSD\PHQWVSHU\HDU Time Value of Money TVM-At a Glance…3D\PHQW 1XPEHURISD\PHQWVSHU\HDUPRGH +RZPXFKFDQ\RXERUURZDWDLQWHUHVWUDWH TVM What if…-At a Glance…DOFXODWHVDPRXQW\RX FDQERUURZ ’LVSOD\VEDODQFH Amortization-At a Glance…DQGBALDQQXQFLDWRUVUHVSHFWLYHO\ ’LVSOD\VSULQFLSDO FRPSRXQGHGPRQWKO\ Interest Rate Conversion-At a Glance…WKHQVROYHIRUWKHXQNQRZQUDWH 3HULRGVSHU\HDU QWHUV ,5 IRR/YR and NPV-At a Glance…1HWSUHVHQWYDOXH QWHUVQXPEHURIFRQVHF OHDUVWDWLVWLFDOUHJLVWHUV Statistics-At a Glance… 55.68 10.00 27.50 420.00 Key memory Backspace Accumulate statistical data Cash flows Keyboard MapPage Simple Arithmetic Calculations Power On and OffAdjusting the Display Contrast Getting Started DOFXODWHVUHVXOW KDQJHVWKHVLJQRI Clearing Memory Understanding the Display and KeyboardCursor Clearing the Calculator 26 1 Getting Started Annunciators DJDLQ Shift KeyStatistics Key EHHQSHUIRUPHG $GGVDQG Math FunctionsInput Key Swap Key FKDQJH Display Format of NumbersQWHUV QXPEHU DOFXODWHVWKHSHUFHQW SODFHV Specifying Displayed Decimal PlacesScientific Notation DIWHUWKHGHFLPDOSRLQW ’LYLGHV Displaying the Full Precision of NumbersInterchanging the Period and Comma GHFLPDOSRLQWLVQRWVKRZQ Rounding Numbers Messages Finding a Percent Business PercentagesPercent Key Percent Change Adding or Subtracting a Percent GLVSOD\HG Margin and Markup CalculationsMargin Calculations Markup on Cost Calculations FDVHRIVRXS Using Margin and Markup Together6WRUHVPDUNXS DOFXODWHVWKHSULFHRQ RSHUDWLRQV Using Stored Numbers in CalculationsUsing Constants Number Storage and Arithmetic VWDQW FRQVWDQW UHJLVWHU Using the M RegisterUHJLVWHU 5HFDOOVFRQWHQWVRIWKH RPSOHWHVILUVW Using Numbered RegistersIROORZLQJ 5HFDOOV5 LQ5 Doing Arithmetic Inside Registers0XOWLSOLHVLQ5 E\ DQGVWRUHVUHVXOW Doing Arithmetic ⋅ Power OperatorUsing Parentheses in Calculations FDOFXODWH 1RFDOFXODWLRQ\HW DOFXODWHV†DOFXODWHV 0XOWLSOLHVWKHUHVXOWE\ WRVROYLQJDILQDQFLDOSUREOHP Picturing Financial ProblemsHow to approach a Financial Problem Picturing Financial Problems 000.00 46 4 Picturing Financial ProblemsSigns of Cash Flows DERXWWKHWUDQVDFWLRQ NQRZQEHIRUH\RXFDQEHJLQFDOFXODWLQJ Periods and Cash FlowsSimple and Compound Interest Simple Interest 005.00 010.03 015.08 020.16 025.26 48 4 Picturing Financial ProblemsCompound Interest DUHEDVHGRQFRPSRXQGLQWHUHVW Interest Rates Two Types of Financial ProblemsRecognizing a TVM Problem PMT = -1,041.40 FV = -10,000.00 PV = 150,000.00= 360 30 357 358 359 000.00 Recognizing a Cash Flow ProblemPage 3D\PHQWVPXVWRFFXUDWUHJXODULQWHUYDOV Using the TVM ApplicationTime Value of Money Calculations 7RXVH790VHYHUDOSUHUHTXLVLWHVPXVWEHPHW RFFXUDWWKHEHJLQQLQJRUHQGRIHDFKSHULRG Clearing TVMDOFXODWHVDQDPRUWLDWLRQWDEOH RFFXUVDWWKHEHJLQQLQJRIWKHILUVWSHULRG Loan Calculations Begin and End Modes WRSD\DIWHU\HDUV 6WRUHVDPRXQWERUURZHG 6WRUHVWKHDPRXQWOHIW 6WRUHVLQWHUHVWUDWH PV = ? YR = 7.5% = 30 356 357 358 359 360 PMT = End ModeSXUFKDVHSULFH 6HWVSHULRGVSHU\HDU 6WRUHVRULJLQDOORDQ 6ROYHWKLVSUREOHPXVLQJWZRVWHSV6WRUHVORDQEDODQFH DIWHU\HDUV PV = 172,500.00 YR = 8.8% = 4 WKHQVWRUHV WRDFFXPXODWH Savings CalculationsOHDUVDOOUHJLVWHUV ILUVWGHSRVLW PMT = PV = -2,000.00 FV= ? YR = 6.3%YR = GHSRVLWV FV = YR = 7% = 600 50 PV = -400,000.00 Begin ModeSHU\HDU 6WRUHVQXPEHURI WKHEHJLQQLQJRIHDFK Lease CalculationsZLWKGUDZDOV WZRFRPPRQOHDVHFDOFXODWLRQV LQPRQWKV FV = 7,500.00 PMT = ? YR = 10% PV = -13,500.00 Begin Mode\LHOG YDOXH PMT = -2,400.00 48th payment due up front FV = -15,000.00 Begin Mode PV = ?7KLVVROXWLRQUHTXLUHVIRXUVWHSV $GGVDGGLWLRQDO SD\PHQWVDOFXODWHVSUHVHQW YDOXHRIPRQWKO\ Principal $ Interest $ Time AmortizationPayment $ 68 5 Time Value of Money Calculations WKHVDPHYDOXHVDJDLQDQGEDODQFH \WKHVWDUWLQJDQGHQGLQJSD\PHQWVWKDWZLOOEHDPRUWLHG HQGLQJSHULRGV 579.82’LVSOD\VWKH35,113,894.66’LVSOD\VWKH,17 178,420.18’LVSOD\VWKH%$/ 70 5 Time Value of Money Calculations $PRUWLHWKHVHFRQG\HDU’LVSOD\V35,1DQGWKH 6HWVSD\PHQWVSHU\HDU ’LVSOD\V,17DQGWKHLQWHU HVW SULQFLSDOSD\PHQW IDYRUDEOHLQWHUHVWUDWH Interest Rate ConversionsInvestments With Different Compounding Periods SHULRGGLIIHU 6WRUHVQRPLQDOUDWH Compounding and Payment Periods Differ6WRUHVQRPLQDOUDWH 6WRUHVTXDUWHUO\ FRPSRXQGLQJSHULRGV 6WRUHVQRPLQDOUDWH 6WRUHVPRQWKO\FRP SRXQGLQJSHULRGV DOFXODWHVEDODQFHDIWHU Step . &DOFXODWHWKHIXWXUHYD XH6WRUHVSD\PHQW 6WRUHVWRWDOQXPEHURI QWHUWKHQXPEHURISHULRGVSHU\HDU How to Use the Cash Flow ApplicationCash Flow Calculations WKH+3%,, 0RQWKO\\LHOG QWHUVQHWFDVKIORZQWHUVILQDOFDVKIORZ QRPLQDO\LHOG Organizing Cash Flows NPV and IRR/YR Discontinuing Cash Flows 3UHVV*&WRFOHDUWKHUHVLVWHUV Entering Cash FlowsIORZVXVLQJWKHIROORZLQJVWHSV EHHQHQWHUHG 7RYLHZDFDVKIORZSUHVV Viewing and Replacing Cash FlowsJURXSDPRXQW QWHUVQXPEHURI UHSHWLWLRQV IORZJURXSDPRXQW QWHUVQXPEHURI UHSHWLWLRQV Calculating Net Present Value7RUHSODFHDFDVKIORZDPRXQWSUHVV 7KHVHVWHSVGHVFULEHKRZWRFDOFXODWH139 YR = 15% 10,000 500 OHDUVUHJLVWHUVQWHUVQXPEHURI RFFXUUHQFHV 82 6 Cash Flow Calculations FDOFXODWHWKHQHWSUHVHQWYDOXH 000 10,000 500 28,000 11 13 15 17 IRR/YR = ? 19 21 23 Calculating Internal Rate of Return 3UHVV*9 SUHYLRXVHDPSOH 84 6 Cash Flow Calculations Automatic Storage of IRR/YR and NPV Statistical Calculations Statistical CalculationsClearing Statistical Data HLJKWHGPHDQ VWDWLVWLFDOUHJLVWHUV Two-Variable Statistics and Weighted MeanEntering Statistical Data One-Variable Statistics Correcting Two-Variable Data Correcting Statistical DataSummary of Statistical Calculations Correcting One-Variable Data 88 7 Statistical Calculations LI\RXHQWHUHG\GDWD6XPRIWKHYDOXHV 6XPRIWKH\YDOXHV DOFXODWHVWKHURRWPHDQ VTXDUH 90 7 Statistical Calculations Linear Regression and Estimation82.75 ’LVSOD\VPHDQRIZHLJKWV\ IROORZV 783.25VWLPDWHVVDOHVLI ’LVSOD\VVORSHFRHIILFLHQW PLQXWHVRIDGYHUWLVLQJ 357.38VWLPDWHVVDOHVLI Weighted Mean Page SURGXFW Setting a Sales PriceAdditional Examples Business Applications OHDUVVWDWLVWLFVUHJLVWHUV Forecasting Based on HistoryVHYHQ VWLPDWHVVDOHVIRU\HDU Cost of Not Taking a Cash Discount 17567 Loans and MortgagesSimple Annual Interest Continuous Compounding Yield of a Discounted or Premium Mortgage DOFXODWHVUHJXODU PRUWJDJHQWHUVDPRXQWOHIWWRSD\ DIWHU\HDUV Annual Percentage Rate for a Loan With Fees GXH 72&DOFXODWHV$35FRQVLGHULQJIHHV LQWHUHVWD HPDGH Loan With a Partial Odd First Period UHEDWH LWKZKLFKFKRLFHGR\RXSD\OHVVIRUWKHFDU Automobile LoanDPRXQW GHDOHULVRIIHULQJWZRFKRLFHVIRUILQDQFLQJ Canadian Mortgages 106 8 Additional Examples What if … TVM CalculationsIROORZV 6WRUHVQHZWHUP LQWHUHVWSDLGRQWKHFRQWUDFWWRSD\RIIORDQ ELZHHNO\SD\PHQWV Year SavingsSaving for College Costs $15,000 YR = 9% 142 143 144 PMT = ? 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