Chapter006_Formulas_2nd

025 or 25 per quarter dividend for new preferred 100

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Unformatted text preview: rs? for Money chimp assumes annuity due!!! Payment = \$313,497.81 38 Table 6.2 39 Effective Annual Rate (EAR) This is the actual rate paid (or received) after This accounting for compounding that occurs during the year the If you want to compare two alternative If investments with different compounding periods you need to compute the EAR and use that for comparison. comparison. 40 Annual Percentage Rate This is the annual rate that is quoted by law By definition APR = period rate times the number of By periods per year periods Consequently, to get the period rate we rearrange the Consequently, APR equation: APR Period rate = APR / number of periods per year You should NEVER divide the effective rate by the You number of periods per year – it will NOT give you the period rate period 41 Computing APRs What is the APR if the monthly rate is .5%? What is the APR if the semiannual rate is .5%? .5(12) = 6% .5(2) = 1% What is the monthly rate if the APR is 12% with What monthly compounding? monthly 12 / 12 = 1% 42 Things to Remember You ALWAYS need to make sure that the interest rate You and the time period match. and If you are looking at annual periods, you need an annual If rate. rate. If you are looking at monthly periods, you need a monthly If rate. rate. If you have an APR based on monthly compounding, If you have to use monthly periods for lump sums, or adjust the interest rate appropriately if you have payments other than monthly payments 43 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% 44 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 45 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? 46 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. 47 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 48 1 m -1 APR - Ex...
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This document was uploaded on 10/01/2013.

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