Cash Flow – Student Load Example

Question:

Mary borrows $100k from the government for graduate school at an annual interest rate = 6%. The interest starts accruing now but she only has to pay back after she graduates 5 years later. She’s expected to make 10 year-end-payments after she’s graduated. What is the annual payment?

Answer:

As usual, the first thing to deal with cash flow problem is to draw a timeline and label the known and unknown cash flows. In this question, at t=0, there is an inflow of the loan equals to 100k. At t=5, 5 years later from now, she will graduate. At the end of the 6^th year (t=6), she will start paying the loan. This is a cash flow problem. The difficulty is that in the first 5 years, there are no cash flows as she doesn’t need to pay anything before graduation. But the second part resembles a simple amortization question. What we can do is to find the equivalent time value of the 100k she receives now at t=5. This can be easily calculated as 100k*(1+6%)⁵

= 133.8k. Therefore, we have converted this irregular cash flow problem to a simple amortization problem with present value = 133.8k, interest rate per year =6%, N = 10 years, future value = 0. This gives annual payment = 18.2k.