Question

You are planning to make monthly deposits of $100 into a retirement account that pays 7 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 24 years?

Multiple Choice

$892,682.82

$69,812.00

$70,670.72

$78,109.75

$74,390.23

Answer 1

Answer 2

SOLUTION :

Monthly compounding.

Monthly deposit, A = 100 ($) (starting from the next month)

Monthly interest rate, r = 7/12 % = 7/1200 in fractions.

=> 1 + r = 1207/1200 

Periods, n = 24 * 12 = 288 months

So, 

FV after 24 years (288 months)

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

= 100 * ((1207/1200)^288 - 1) / (7/1200)

= 74390.23 ($)  : 5th OPTION (ANSWER).