Question

# A person deposits \$275 at the end of each month in an account which earns 9.5%...

A person deposits \$275 at the end of each month in an account which earns 9.5% compounded monthly for 29 years. The person then stops making the deposits, but allows the money to remain in the bank earning the same interest for 6 more years.

a. Find the value of this account at the end of 35 years.
\$

b. State the total amount of interest earned on this account.
\$

Solution

a. Here first we need to find the future value of annuity payments at the end of 29 years

Future value of annuity=Annuity amount*(((1+r)^n-1)/r)

where

n= number of periods=29*12=348

r=rate of intrest per period=9.5/12=0.79166667% per month

Annuity payment=275

Future value of annuity=275*(((1+.0079166667)^348-1)/.0079166667)

=505470.413

Now this amount will again remain deposited for further 6 years

Future value=Principal*(1+r)^n

Principal=505470.413

n= number of periods=6*12=72

r=rate of intrest per period=9.5/12=0.79166667% per month

Future value=505470.413*(1+.0079166667)^72=891802.86 (Value of his account after 35 years)

b Total intrest earned =Value of his account after 35 years-Amount deposited

=891802.86-348*275

=796102.86 (Total interest earned)