Question

1.

A)

The Mellows 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 14 years, what will be the size of the monthly payments? Round to the nearest cent

B)

Answer 1

A.)

Beginning Investment 20,000 rate of interest = 3% compounded monthly annuity payments are made after 14 years annual effective interest rate = (1+0.03/12)^12-1 so the value of annuity at the end of 14 years 3.04% 20000*(1+0.0304)^14 30416.69 Now this ammount has to be paid over 4 years every month Present value= 30416.69 Interest rate (I/Y) = 3.04/12 0.253333 Future value 0 Number of payments 4*12 48 now calculate PMT (monthly payment) by using financial calculator 673.79

B).

Interest rate is 3% compounded semiannually Annual effective Interest rate |(1+0.03/2)^2-1 0.030225 3.02% Periodic payment (PMT) 1000 Number of payments (N) 7*12 = 84 future value 0 Interest rate (I/Y) = 3.02/12 = 0.251667 Use financial calculator to calculate the present value 75629.72 Now, the first withdrawal is made after 4 years 1 month that means the withdrawal is made at the end of first period, so the present value 75629.72/(1.0302) ^4 67143.86