Question

# Mike is currently 10 years old and his parents are planning the finance of his college...

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)

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