Question

Background: Suppose you will go to graduate school for 3 years beginning in year 5. Tuition is $25,109 per year, due at the end of each school year. Assume annual compounding. In the above description, if you see a flat yield curve of 0.08 for example, then it means that the yield at all maturities is 8%.

Question: Suppose in the question above, the tuition obligations have a Macaulay duration of 6.36 in years, and that you wish to immunize against the tuition payments by buying a single issue of a zero coupon bond. What maturity zero coupon bond should you buy? Assume annual compounding. Round your answer to 2 decimal places.

Answer 1

First let understands what is Maculay duration, it is measure how much time it will take for investor to get it bond price back in form of interest and principal repayments, at same it is also a measure of sensitivity. It is different from maturity because calculated using weights of present values of prinicpal and interest payments.

In case of zero coupon bonds, which make single payment at time of maturity , Macaulay duration and maturity are same. It is because it doesn't make and periodic interest payment.

So as given in question we need to find a maturity of zero coupon bond, which equals macaulay duration of 6.36, so it will be maturity of 6.36.