Calculate the duration of a five-year bond with face value $1000,fixed coupon of 8% per annum,with current market yields of 9%.
A) 4.13 years
B) 4.30 years
C) 4.72 years
D) 5.00 years

Question

Quizplus · Accepted Answer

To calculate the duration, we need to first calculate the present value of the bond using the current market yield (discount rate) of 9%.

PV = 80/1.09 + 80/(1.09)^2 + ... + 1080/(1.09)^5 
PV = $872.35

Next, we need to calculate the sum of the present value of the cash flows multiplied by their respective time periods, and divide by the bond's price:

Duration = (1/872.35) x [80/1.09 + 2(80/1.09^2) + 3(80/1.09^3) + 4(80/1.09^4) + 5(1080/1.09^5)] 
Duration = 4.303 years

Therefore, the closest option is B) 4.30 years.

Calculate the Duration of a Five-Year Bond with Face Value