Question

Question is from:

Corporate Finance (4th Edition)

Chapter 5, Problem 10P

Your son has been accepted to college. The college guarantees that your son's tuition will not increase for the four years that he attends college. the first 10,000 payment is due every six months until you have made a total payment of eight payments. The college offers a bank account that allows you to withdraw money every six months and has a fixed APR of 4% (semiannual) guaranteed to remain the same over the next four years. How much must you deposit today if you intend to make no further deposits and would like to make all the tuition payments from this account, leaving the account empty when the last payment is made?

Hi, Can you please help me understand why the answer is less than the value of the 8*10,000 tuition payments? intuitively it seems like it should be greater than 80,000 since there is APR charged and the tuition costs alone are 10,000 each.

Thank you, Elliot

Answer 1

Obviously, the answer has to be less than 80,000 since we are depositing it one time in a bank which will offer us interest with interest rate of 4% (semiannual). Hence our initial principle amount will grow during the course of 4 year and we will be able to pay all the 8 installments.

We will first draw the cash flow diagram and then carry on with calculations. Now, there can be 2 cases, first, where first payment is due now, and second, where first payment is due in 6 months from now. I have solved both cases since it is not very clear in question.

Please do rate me and mention doubts, if any, in the comments section .