Question

Your smart daughter has just turned 6 years old, and she plans to attend college at age 18.

Current education costs per year are $24,000. These costs are expected to grow at a rate of

3% per year for the next 15 years. Assuming that your daughter will spend 4 years in college

and that the effective annual interest rate for the next 20 years is 8%, what is the fixed

annual amount that you have to put away each year for the next 11 years starting a year

from today to pay for her education? Assume that you’ll pay the tuition at the

beginning

of

each college year.

Answer 1

Let fixed amount each year for next 11 years be x

Then present value of savings=x/0.08*(1-1/1.08^11)

Present value of withdrawals=24000*1.03^12/1.08^12+24000*1.03^13/1.08^13+24000*1.03^14/1.08^14+24000*1.03^15/1.08^15=50694.72578

Present value of savings must equal present value of withdrawlas

Hence x/0.08*(1-1/1.08^11)=50694.72578

=>x=7101.132

So, fixed amount each year=$7101.132