Question

You are to make monthly deposits of $450 into a retirement account that pays 10.7 percent interest compounded monthly. Required: If your first deposit will be made one month from now, how large will your retirement account be in 32 years? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)   Annuity future value $

Answer 1

that will be

450*[(1+r)^n -1]/(r)

here r = 0.107/12 = 0.0089167

and n= 32*12 = 384

putting these values

Annuity future value = 1475138.3

Answer 2

SOLUTION ;

Monthly compounding.

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

Monthly deposit, A = 450 ($)

Monthly interest rate , r = 10.7/12 % = 10.7/1200 in fractions.

=> 1 + r = 1 + 10.7/1200 = 1210.7/1200

Monthly periods, n = 32 * 12 = 384months.

So,

Amount in the account after 32 years (384 months) as per ordinary annuity formula :

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

= 450((1210.7/1200)^384 - 1) / (10.7/1200)

= 1475143.62 ($) (ANSWER).