Question

A bond has three years to maturity. It pays a 10% coupon rate annually, a $1000 face value, and the market rate of interest is 8%. What is the duration of the bond?

Answer 1

Cash flow in each of the first two years = Coupon rate * face value = 10% * 1000 = $ 100

Cash flow in the third year = Principal + Coupon = 1000 + 100 = $ 1100

PV of cash flow in 1st period = 100/(1+10%) = 100/(1+ 10%) = $ 90.91

PV of cash flow in 2nd period = 100/(1+ rate)^2 = 100/(1+10%)^2 = $ 82.64

PV of cash flow in 3rd year = 1100/(1+10%)^3 = $ 826.45

Duration = (PV of cash flows * Period = (90.91 * 1 + 82.64* 2 + 826.45 * 3) /PV of cash flows) =

(2735.54/1000) = 2.735