Question

The Calvarusos have decided to invest in a college fund for their young son. They invested $20,000 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 12 years, what will be the size of the monthly payments?

Answer 1

Effective monthly rate, r = 3%/12 = 0.0025

First, let's find the future value of the invested amount in 12 years

FV12 = PV * (1 + r)^n

r = 0.0025

n = 12 * 12 = 144 months

FV12 = 20,000 * (1 + 0.0025)^144

FV12 = 20,000 * 1.4326856339

FV12 = $28,653.712678

Now, with this as the PV let's find the size of the monthly payments for 4 years

Number of monthly payments = 4 * 12 = 48

r = 0.0025

PV = 28,653.712678

The size of the monthly payments is $632.6490234754