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# Hints+on+Homework+2 - amount P at the end of one payment...

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IOE 201 - Economic Decision Making Homework #2 - Hints for Problems 7 and 8 In Problems 7 and 8, the payment period is different than the interest period. Let r = nominal annual interest rate M = number of interest periods per year i = interest per interest period The interest rate per interest period i = r / M . However, it is the interest rate per payment period that is the interest rate needed in the formulas for equal payment series. \$3000 \$3000 \$3000 \$3000 12 1 2 3 4 5 6 7 8 9 0 10 11 Interest Period Payment Period In Problem 7, the payment period = ¼ year. So the number of interest periods per payment period = M /4 (e.g., in Problem 7(b), M = 12, so there are 3 interest periods per payment period) Since there are M /4 interest periods in every payment period, the future worth of an
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Unformatted text preview: amount P at the end of one payment period is P (1 + i ) M /4 , and so the interest in that one payment period is P (1 + i ) M /4-P = P {(1 + i ) M /4-1}. Therefore, the interest rate per payment period is (1 + i ) M /4-1 = 1 1 4- + M M r In the continuous compounding case in Problems 7(c) and 8, M → ∞ , and so the interest rate per payment period is 1 1 lim 4- + ∞ → M M M r = 1 1 lim 4 1- + ∞ → M M M r = 1 4-r e Since payment period = ¼ year, the total number of payments in n years is N = 4 n See also textbook, pp. 91-92....
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