Question

You are planning to make monthly deposits of $90 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 will your retirement account be in 27 years?

Answer 1

Solution:
	Value of retirement account be in 27 years is     $123,076.25
Working Notes:
	Value of retirement account be in 27 years is the future value of annuity of monthly deposit.
	Future value of annuity = P x ((1+i)^n - 1)/i
	P= Monthly deposits= $90
	i= monthly rate =APR/12 = 9%/12 = 0.75%
	n= no. Of payments x no. Of years
	= 12 x 27 =324
	Future value of annuity = Value of retirement account be in 27 years
	Future value of annuity
	= P x ((1+i)^n - 1)/i
	= 90 x ((1+0.75%)^324 - 1)/0.75%
	=$123,076.2532
	=$123,076.25
	Value of retirement account be in 27 years is $	123,076.25
Please feel free to ask if anything about above solution in comment section of the question.

Answer 2

SOLUTION ;

Monthly compounding.

First deposit will be made one month from now.So, it is ordinary annuiy case.

Monthly deposit, A = 90 ($)

Monthly interest rate , r = 9/12 % = 3/4% = 3/400 in fractions.

=> 1 + r = 1 + 3/400 = 403/400

Monthly periods, n = 27 * 12 = 324 months.

So,

Amount in the account after 27 years (324 months) as per ordinary annuity :

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

= 90((403/400)^324 - 1) / (3/400)

= 123076.25 ($) (ANSWER).