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# Lec7 - Lecture 7 page 43 TIME VALUE OF MONEY What we want...

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Lecture 7 page 43 T IME V ALUE OF M ONEY What we want to be able to do: determine how much we must invest today to obtain a specified amount in the future (saving for retirement or for college) determine the expected rate of return on an investment when we know (or estimate) the future cash flows (return on a bond or project) determine the periodic payment on an amortizing loan (mortgage, student loan, or automobile loan) compare investment opportunities with different cash flow characteristics (bank CDs, stocks, projects) determine the number of years needed to accumulate a certain amount or to pay off a loan (saving for a down payment on a home or for a new car) 3 Critical Variables principal interest or return time Compound Interest We use compounding, or compound interest to reflect the fact that many investments earn interest on interest. Use a timeline for all TVM problems...it will make your life easier!! - Richard T. Bliss, Babson University and Terry D. Nixon, Miami University

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Lecture 7 page 44 Lump-sum Future Value and Present Value Definitions: PV → Present Value FV → Future Value I or r → annual (interest) rate (annual percentage rate or APR ) M → number of compounding periods per year; the frequency of compounding I/M or r/M → intraperiod, or periodic interest rate N → total number of periods (M × number of years) Future Value If we put \$100 in the bank today and earn interest of 5% per year (annual compounding), what do we have after two years? TIMELINE: First year: \$100 × (1 + .05) = \$1 × 1.05 = \$105, or our original \$100 plus \$5 interest.
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