Question

An insurance company is analyzing the following three bonds, each with five years to maturity, annual interest payments, and is using duration as the measure of interest rate risk.

Answer 1

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

Answer 2

Answer:

Check explanation.

Explanation:

======> NB: Kindly check the attachment (picture) for the formula for Calculating the duration.

Okay, let us continue solving the question; the maturity of the bonds is in five (5) years.

(a). Per value= $10,000 coupon rate= 8%, r= 0.10, (b). Per value= $10,000 coupon rate= 10%, r= 0.10, (c). Per value= $10,000 coupon rate= 12%, r= 0.10.

Therefore, using the formula from equation (***) in the attached picture, we can calculate for the duration.

Also, in the attached picture you will find the solution to the question.

The solution to the question is; (a).4.28 years, (b). 4.1 years, (c) 4.2 years.