Question

What is the duration of a bond that has a 6% coupon paid semi-annually and matures...

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.

Homework Answers

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

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