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.

What is the duration of each of the three bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

a. $10,000 par value, coupon rate= 8.5%, rb=0.15. ___ years

b. $10,000 par value, coupon rate = 10.5%, rb=0.15 4.02 years

c. $10,000 par value, coupon rate 12.5%, rb = 0.15. ____ years

Pease help me find a. and b.

Answer 1

1.
=(1*8.5/1.15+2*8.5/1.15^2+3*8.5/1.15^3+4*8.5/1.15^4+5*8.5/1.15^5+5*100/1.15^5)/(8.5/1.15+8.5/1.15^2+8.5/1.15^3+8.5/1.15^4+8.5/1.15^5+100/1.15^5)
=4.17039079

2.
=(1*10.5/1.15+2*10.5/1.15^2+3*10.5/1.15^3+4*10.5/1.15^4+5*10.5/1.15^5+5*100/1.15^5)/(10.5/1.15+10.5/1.15^2+10.5/1.15^3+10.5/1.15^4+10.5/1.15^5+100/1.15^5)
=4.05610046

3.
=(1*12.5/1.15+2*12.5/1.15^2+3*12.5/1.15^3+4*12.5/1.15^4+5*12.5/1.15^5+5*100/1.15^5)/(12.5/1.15+12.5/1.15^2+12.5/1.15^3+12.5/1.15^4+12.5/1.15^5+100/1.15^5)
=3.95853663