Question

Find the duration of a bond that sells for $87 in the market. The bond pays semiannual coupons of $3 and the principle is $100. The bond matures in 4 years.

Answer 1

In order to determine the Macauly we must complete the following table:

period cash flow PV of Period x

cash flow PV cash flow

1 $3 $2.91 $2.91

2 $3 $2.83 $5.66

3 $3 $2.75 $8.25

4 $3 $2.67 $10.68

5 $3 $2.59 $12.95

6 $3 $2.51 $15.06

7 $3 $2.44 $17.08

8 $103 $81.31 $650.48

Total $723.07

Macauly duration = $723.07 / $87 = 8.31

Modified Macauly duration = Macauly duration / (1 + r) = 8.31 / 1.03 = 8.07