Suppose you deposit 1000 at the end of each quarter for five

Suppose you deposit $1,000 at the end of each quarter for five years at an interest rate of 9% compounded monthly. Which of the following formulas will determine the equal annual end-of- year deposit amount that would accumulate the same balance over five years under the same interest compounding as the $1,000 deposited quarterly? (a) A= [$1,000 (FIA,2.25%, 20)] x (A/F, 996, 5). (b) A= $4,000 (F/A, 9%, 5) (c) A= $1,000 (FIA, 9%/12, 20) x (A/F, 996, 5) (d) None of the above.

Solution

Correct option is (a).

Quarterly interest rate = 9% x (1/4) = 2.25%

Number of quarters = 4 x 5 = 20

Future worth (FW) of quarterly deposits = $1,000 x F/A(2.25%, 20)

Corresponding equal annual deposit = FW x A/F(9%, 5) = $1,000 x F/A(2.25%, 20) x A/F(9%, 5)