Here's the complete question:
An insurance company is analyzing the following three bonds, each with five years to maturity, and is using duration as its measure of interest rate risk:
a. $10,000 par value, coupon rate = 8%, rb = 0.10
b. $10,000 par value, coupon rate = 10%, rb = 0.10
c. $10,000 par value, coupon rate = 12%, rb = 0.10
What is the duration of each of the three bonds?
a. Duration on 8% coupon bond = 4.28 years
Year 1 ,2,3,4,5
CFs 800,800,800,800,10800
DCFs 727.27, 661.2, 601.05, 546.41 6705.95
PV=9241.84
Duration = <DCFs/PV
(7271+661.22+601.053+546.414+6705.95*5)/9241.84
=39568.1/9241.84
=4.2814
b. Duration on 10% coupon bond = 4.17 yearsc.
c. Duration on 12% coupon bond = 4.07 years
