To determine To calculate: The total amount earned in the account. Explanation Given: The first annuity at the end of each month is $400, the first term of annuity is 10 years, interest earned is 4%. Next annuity at the end of each month is $600, the next term of annuity is 10 years, interest earned is 6%. Formula Used: The amount earned 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: Case 1: Calculate the first future value ( S 1 ) on first 10 years payments, by using the above formula. Here, interest earned on the amount is monthly. So, divide interest by 12 and multiply the number of years by 12. R = $ 400 , i = .04 12 n = 12 × 10 = 120 S 1 = R [ ( 1 + i ) n − 1 i ] = $ 400 [ ( 1 + .04 12 ) 120 − 1 .04 12 ] = $ 400 [ ( 1 + .0033 ) 120 − 1 .0033 ] = $ 400 [ 1.4908326 − 1 .00333333 ] Simplifying it further, S 2 = $ 400 [ 0.4908326 0.00333333 ] = $ 400 × 147.2498045 = $ 58 , 899.92 Case2: Now, future value (S 2 ) for next 10 years: Here, interest earned on the amount is monthly. So, divide interest by 12 and multiply the number of years by 12. R = $ 600 , i = .06 12 n = 12 × 10 = 120 S 2 = R [ ( 1 + i ) n − 1 i ] = $ 600 [ ( 1 +

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

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

Publisher: PEARSON

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Chapter 5.3, Problem 9E

To determine

To calculate: The total amount earned in the account.

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Chapter 5 Solutions

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

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