Compounding and Payment Periods Differ

First Bank
Keys:*	Display:
*b	6.70
	4.00
*Z
	6.87
*
Second Bank
*b	6.65
	12.00
*Z
	6.86
*
Third Bank
*b	6.63
	360.00
*Z
	6.85

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5: Time Value of Money Calculations 73

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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 = ? 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5: Time Value of Money Calculations 73

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