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F.Chap06

# Rate if you are looking at monthly periods you need a

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Unformatted text preview: her than monthly payments 41 41 Computing EARs - Example Suppose you can earn 1% per month on \$1 invested Suppose today. today. What is the APR? 1(12) = 12% How much are you effectively earning? • FV = 1(1.01)12 = 1.1268 • Rate = (1.1268 – 1) / 1 = .1268 = 12.68% Suppose if you put it in another account, you earn 3% Suppose per quarter. per What is the APR? 3(4) = 12% How much are you effectively earning? • FV = 1(1.03)4 = 1.1255 • Rate = (1.1255 – 1) / 1 = .1255 = 12.55% 42 42 EAR - Formula m APR EAR = 1 + −1 m Remember that the APR is the quoted rate m is the number of compounding periods per year 43 43 Decisions, Decisions II You are looking at two savings accounts. One pays You 5.25%, with daily compounding. The other pays 5.3% with semiannual compounding. Which account should you use? you First account: • EAR = (1 + .0525/365)365 – 1 = 5.39% Second account: • EAR = (1 + .053/2)2 – 1 = 5.37% Which account should you choose and why? 44 44 Decisions, Decisions II Decisions, Continued Continued Let’s verify the choice. Suppose you invest Let’s \$100 in each account. How much will you have in each account in one year? in First Account: • Daily rate = .0525 / 365 = .00014383562 • FV = 100(1.00014383562)365 = 105.39 Second Account: • Semiannual rate = .0539 / 2 = .0265 • FV = 100(1.0265)2 = 105.37 You have more money in the first account. 45 45 Computing APRs from EARs Computing If you have an effective rate, how can you If compute the APR? Rearrange the EAR equation and you get: equation (1 + EAR) APR = m 1 m -1 46 46 APR - Example Suppose you want to earn an effective rate of Suppose 12% and you are looking at an account that compounds on a monthly basis. What APR must they pay? they [ APR = 12 (1 + .12) or 11.39% 1 / 12 − 1 = .1138655152 47 47 Computing Payments with Computing APRs APRs Suppose you want to buy a new computer system and Suppose the store is willing to sell it to allow you to make monthly payments. The entire computer system costs \$...
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