Question

You are planning to make monthly deposits of $330 into a retirement account that pays 8 percent annual interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 25 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Information provided:

Monthly deposit= $330

Interest rate= 8%/12= 0.6667% per month

Time= 25 years*12= 300 months

The question is solved by calculating the future value.

Enter the below in a financial calculator to compute the future value:

PMT= 330

N= 300

I/Y= 0.6667

Press the CPT key and FV to compute the future value.

The value obtained is 313,838.71.

Therefore, the retirement account will be $313,838.71 in 25 years.

In case of any query, kindly comment on the solution.

Answer 2

SOLUTION ;

Monthly compounding.

First deposit will be made one month from now. So, ordinary annuity case.

Monthly deposit, A = 330 ($)

Monthly interest rate , r = 8/12 % = 2/3% = 2/300 in fractions.

=> 1 + r = 1 + 2/300 = 302/300

Monthly periods, n = 25 * 12 = 300 months.

So,

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

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

= 330((302/300)^300 - 1) / (2/300)

= 313838.71 ($) (ANSWER).