Explanation Given: The first annuity at the end of each quarter is $1000, the first term of annuity is 10 years, interest earned is 4.2%. Next annuity at the end of each quarter is $1500, the next term of annuity is 15 years, interest earned is 7.4%. 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 fist 10 years payments, by using above formula. Here, interest earned on the amount is quarterly. So, divide interest by 4 and multiply the number of years by 4. R = $ 1000 , i = .042 4 n = 4 × 10 = 40 S 1 = R [ ( 1 + i ) n − 1 i ] = $ 1000 [ ( 1 + .042 4 ) 40 − 1 .042 4 ] = $ 1000 [ ( 1 + .0105 ) 40 − 1 .0105 ] = $ 1000 [ 1.518632584 − 1 .0105 ] Simplifying it further, S 2 = $ 1000 [ 0.518632584 0.0105 ] = $ 1000 × 49.39357947 = $ 49 , 393.58 Case 2: Now, calculate future value ( S 2 ) for next 15 years. Here, interest earned on the amount is quarterly. So, divide interest by 4 and multiply the number of years by 4. R = $ 1500 , i = .074 4 n = 4 × 15 = 60 S 2 = R [ ( 1 + i ) n − 1 i ] = $ 1500 [ ( 1 +

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ISBN: 8220106844557

Author: MULLINS

Publisher: PEARSON

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Chapter 5.3, Problem 11E

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To calculate: The total amount earned in the account.

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