Question

The Kucharskis have decided to invest in a college fund for their young son. They invested $30,000 in a deferred annuity that will pay their son at the beginning of every month for 4 years, while he goes to college. If the account earns 3.00% compounded monthly and the annuity payments are deferred for 15 years, what will be the size of the monthly payments?

Answer 1

- Amount Invested today in deferred annuity = $30,000

Calculating the Future valueat the end of year 15 after the deferred period:-

Future Value = Invested amount*(1+r)^n

r = Periodic Interest rate = 3%/12 = 0.25%

n= no of periods = 15 years*12 = 180

Future Value = $30,000*(1+0.0025)^180

Future Value = $30,000*1.56743172467

Future Value = $47,022.95

Now from this account there son will withdraw at the beginning of every month for 4 years.

calculating the amount of withdrawal using PV of annuity due fomula;-

Where, C= Periodic Withdrawal

r = Periodic Interest rate = 3%/12 = 0.25%

n= no of periods = 4 years*12 = 48

C = $1038.23

So, the size of the monthly payments is $1038.23

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