Question

1) 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. What is the Macaulay duration (in years) of your grad school tuitions? Assume a flat yield curve of 0.03.

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%.

Answer 1

Duration = (Present value of a Future cash flows * Year of receipt )/ Present value of a Future cash flows

Year	PVF @ 3%	Cash Flow	PV of Cash flow	Present value of a Cash flows * Year of Reciept
A	B	C	B*C	C*A
5	0.8626	$        25,109	$ 21,659.24	$ 108,296.22
6	0.8375	$        25,109	$ 21,028.39	$ 126,170.35
7	0.8131	$        25,109	$ 20,415.91	$ 142,911.40
		Sum	$ 63,103.55	$ 377,377.97

Duration =

$63,103.55 / $377,377.97

= 5.98 Years