Question

You are planning to make monthly deposits of $80 Into a retirement account that pays 9 percent annual interest (APR), compounded monthly. If your first deposit will be made one month from now, how large wll your retirement account be in 21 years? $713,324.98 $62,415.94 $54,493.95 O $59,443.75 O $56,471.56

Answer 1

N = 21*12, PV = 0, rae = 9%/12 PMT = 80

use FV function in Excel

amount in retirement account = 59,443.75

Answer 2

SOLUTION :

Monthly compounding.

Monthly deposit, A = 80 ($) (starting from the next month)

Monthly interest rate, r = 9/12 % = 9/1200 = 3/400 in fractions.

=> 1 + r = 403/400 

Periods, n = 21 * 12 = 252 months

So, 

FV after 21 years (252 months)

= A((1 + r)^n - 1) / r

= 80 * ((403/400)^252 - 1) / (3/400)

= 59443.75 ($)  : 4th OPTION (ANSWER).