Question

You just had your second child, and you expect her to go to college in 18 yrs. You plan that a four-year college will cost $33,000 each year. The payments are to be made at the beginning of each college year starting at t = 18. Your first child will go to college in 12 years which will cost $25,000 per year with the first payment due at t = 12. You already have $20,000 on an account that pays 8% p.a. You plan to start depositing on that account a fixed amount of money once a year starting at t = 1 and do that until the due date of the last tuition payment for your second child. Find the amount of money that you shall deposit each year.

Answer 1

1]	PV of the fee payable for the 1st child = 25000/1.08^12+25000/1.08^13+25000/1.08^14+25000/1.08^15 =	$                 35,512.86
2]	PV of the fee payable for the 2nd child = 33000/1.08^18+33000/1.08^19+33000/1.08^20+33000/1.08^21 =	$                 29,540.45
3]	Total of PV of college fee for both children	$                 65,053.31
4]	Less: Amount in hand	$                 20,000.00
5]	PV of installments to be made for 21 years	$                 45,053.31
6]	Amount to be deposited each year = 45053.31*0.08*1.08^21/(1.08^21-1) =	$                   4,497.77