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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.

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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

codedmog101

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.

Ver imagen codedmog101
Ver imagen codedmog101
Ver imagen codedmog101

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