Question

What is the duration of a bond that has a 6% coupon paid semi-annually and matures in exactly 3 years if the discount rate is currently 10%? Use Macaully’s Duration.

Answer 1

First we have to calculate the Present value of Bond

Let the Face value of Bond is $100

Since coupon is paid semi-annually,hence

No.of Period=3*2=6

Coupon amount per period=(100*6%)/2

=$3

Discount Rate=10%/2   

=5%

Thus Present value of bond is as follows

Period(d)	Cash flows($)(a)	PVIF@5%(b)	Present Value(a*b)=(c)	C*d
1	3	.952	2.856	2.856
2	3	.907	2.721	5.442
3	3	.864	2.592	7.776
4	3	.823	2.469	9.876
5	3	.784	2.352	11.76
6	3+100=103	.746	76.838	461.0128
Total	498.7228

Now, Macualay duration

=Sum of C*d/Bond price

=$498.7228/100

=4.987 period

=4.987/2

=2.49 years