Question

Ryan has deposited $100 into a retirement account at the end of every month for 50 years. The interest rate on the account is 1.5% compounded monthly. a) How much is in the account after 45 years? b) How much inte rest was earned over the 45 years?

Answer 1

future payment is $77056.92

total interest is paid after 45 year is $23056.42

Explanation:

Given data

payment (P) = $100

No of installment (n) = 12

rate of interest ( r ) = 1.5 % i.e. = 0.015

time period (t) = 45 years

to find out

future payment and interest after 45 year

solution

we know future payment formula i.e. given below

future payment = payment ×
`(1+(r)/(n))^(nt) - 1) / (r/n)`

now put all these value in equation

future payment = $ 100 ×
`(1+(0.015)/(12))^(12*45) - 1) / (0.015/12)`

future payment = $ 77056.92

payment paid in 45 year @ $100 total money is paid is 45 × 12 × $100 i.e. = $54000

total interest = future payment - money paid

total interest = $77056.42 - $54000

total interest = $23056.42