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# Ross6eChap05sm.doc

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McGill University

Management Core

MGCR 341

all

Spring

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Chapter 5 The Time Value of Money51The simple interest per year is5000009450So after 10 years you will have 450104500 in interest The total balance will be 500045009500With compound interest we use the future value formulatFVPV1 r 10FV50001091183682The difference is 1183682950023368252To find the FV of a lump sum we usetFVPV1r10aFV1000106 17908510b FV1000109 23673620cFV1000106 320714dBecause interest compounds on the interest already earned the interest earned in part c is more than twice the interest earned in part a a ie 79085 versus 220714 With compound interest future values grow exponentially53To find the PV of a lump sum we usetPVFV1r6PV15451107 10295659PV51557115 146557218PV886073111 1354116023PV550164118 1222379Answers to EndofChapter Problems5154To answer this question we can use either the FV or the PV formula Both will give the same answer since each is the inverse of the other We will use the FV formula that istFVPV1rSolving for r we get1trFVPV1212FV3072421rr3072421 01263 or 1263919FV8964101rr8964101 0907 or 90715115FV162181517001rr16218151700100792 or 79230130FV483500187501rr48350018750101144 or 114455To answer this question we can use either the FV or the PV formula Both will give the same answer since each is the inverse of the other We will use the FV formula that istFVPV1rSolving for t we getlnFVPVln1tr tFV1284625106tln1284 625ln 1061236 yearstFV4341810113tln4341 810ln 1131374 yearstFV40266218400132tln40266218400ln 1321111 yearstFV17343921500116tln17343921500ln 1161407 years56To find the length of time for money to double triple etc the present value and future value are irrelevant as long as the future value is twice the present value for doubling three times as large for tripling etc To answer this question we can use either the FV or the PV formula Both will give the same answer since each is the inverse of the other We will use the FV formula that istFVPV1rSolving for t we gettlnFVPVln1r The length of time to double your money istFV21109tln 2ln 109804 yearsThe length of time to quadruple your money istFV41109 tln 4ln 1091609 yearsAnswers to EndofChapter Problems52Notice that the length of time to quadruple your money is twice as long as the time needed to double your money the difference in these answers is due to rounding This is an important concept of time value of money57To find the PV of a lump sum we usetPVFV1r20PV75000000010821550658085458 To answer this question we can use either the FV or the PV formula Both will give the same answer since each is the inverse of the other We will use the FV formula that istFVPV1rSolving for r we get1trFVPV114r10311500123775001 00446 or446Notice that the interest rate is negative This occurs when the FV is less than the PV59A consol is a perpetuity To find the PV of a perpetuity we use the equationPVCrPV1200057 PV210526510To find the future value with continuous compounding we use the equationRtFVPVe0125aFV1900e 3462030103b FV1900e 25647300510cFV1900e 3132570078dFV1900e 332628511To solve this problem we must find the PV of each cash flow and then add them To find the PV of a lump sum we usetPVFV1r234PV1012001107301109651101590110350523234PV1812001187301189651181590118294866234PV2412001247301249651241590124262117Answers to EndofChapter Problems53

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