(a) Explanation Given: a) The future value after six years is $8000, the term of annuity is 6 years, interest earned quarterly is 12%. b) The future value after six years is $8000, the term of annuity is 6 years, interest earned quarterly is 8%. Formula Used: Amount to be paid for six years can be calculated by using the formula S = R [ ( 1 + i ) n − 1 i ] S is the future value or total amount earned on annuity, R is the payment at the end of each year, i is the interest rate per year, n is the number of years. Calculation: a) Here, Interest earned on the amount is quarterly. So, divide interest by 4 and multiply the number of years by 4. S = $ 8000 , i = 0.12 4 , and n = 6 × 4 By using above formula, S = R [ ( 1 + i ) n − 1 i ] $ 8000 = R [ ( 1 + .12 4 ) 24 − 1 .12 4 ] $ 8000 = R [ ( 1.03 ) 24 − 1 .03 ] $ 8000 = R [ 2.03279 − 1 .03 ] Simplifying it further, $ 8000 = R [ 1.03279 0.03 ] $ 8000 = R ( 34.4264 ) R = $ 8000 34

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

12th Edition

ISBN: 9780134767628

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 5.3, Problem 4CP

(a)

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To find: The amount of each payment.

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Chapter 5.3, Problem 3CP

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