Question

1. Mike is currently 10 years old and his parents are planning the finance of his college expenses. They will set up a bank account and deposit $X one year from today and will deposit 4% more each subsequent year. The last deposit will be 11 years from today. College expenses of $40,000 will occur 8, 9, 10, and 11 years from today. What is X if all the deposits exactly pay for Mike’s college expenses? Assume the effective annual interest rate is 4%. (10 points)

Answer 1

The first step is to find the size of the college expense for 4 years. The size of the expense is found using present value of annuity equation.

The bank account must have $ 145,195.81 in 11 years to fund the college expense. The deposit X is found using future value of growing annuity equation.

In the above equation, the effective interest rate equals the growth rate. hence the formula reduces to

FV = X *  n * ( 1 + r) ^n-1

$ 145,195.81 = X * 11 * ( 1 + 0.04)^11-1

The value of the deposit X = $ 8917.19 $ 8917.2