Question

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%.

Answer 1

Present Value of deposits=X/1.04+X*1.04/1.04^2....X*1.04^10/1.04^11=X/1.04*11

Present Value of college expenses=40000/1.04^8+40000/1.04^9+40000/1.04^10+40000/1.04^11

Present Value of Deposits must equal Present Value of college expenses

Hence,
X/1.04*11=40000/1.04^8+40000/1.04^9+40000/1.04^10+40000/1.04^11

=>X=(40000/1.04^8+40000/1.04^9+40000/1.04^10+40000/1.04^11)*1.04/11

=>X=10431.85