Question

You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $55,000 per year per child, payable at the beginning of each school year. The annual interest rate is 9.2 percent. How much money must you deposit in an account each year to fund your children’s education? Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume your children will be on the four-year plan.

please show financial calculator way and formula way

Answer 1

Since you want to deposit the money till your second child begin in year 17, the value of your expenses at the beginning of year 17 is calculated as follows

Total expenses required for first child = 55,000*1.092^2 + 55,000*1.092 + 55000 + 55000/1.092 = 231,011.82

Total expenses for second child = 55000 +55000/1.092 + 55000/1.092^2 + 55000/1.092^3 = 193,726.45

Total expenses equired at the beginning of year 17 = 424,738.27

Now, you have 16 years (16 deopsits) to save this amount required at beginning year 17.

This amount will be equal to FV of an annuity given by:

FV A = P*((1+r)^n-1)/r

424,738.27 = P*(1.092^16-1)/0.092

P = 12,652.14

Amount you will need to deposit each year = $12,652.14