Question

A person deposits $45 at the end of each month in an account which earns 12.5% 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 15 more years.

a. Find the value of this account at the end of 44 years.
$  

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

Answer 1

Hi

Here monthly deposit C = $45

time t in months = 29*12 = 348 months

rate r (monthly) = 12.5%/12 = 1.04%

So value after 29 years F = (C/r)*((1+r)^t-1)

=(45/1.04%)*(1.0104^348-1)

=4320*35.8277

=$154,775.60

Now we have to find value after 44 years

so now Value after 29 years P = $154,775.60

time t = 44-29 = 15 years = 15*12 =180 months

monthly rate r = 1.04%

a ) So Value after 44 years = 154775.60*(1+0.0104)^180

=154775.60*1.0104^180

=154775.60*6.4579

=$999,522.84

b) Interest = 999,522.84 - 45*348

= 999,522.84 - 15660

=$983,862.84

Thanks

Thanks