Question

You were asked to calculate the duration of a 10 year bond that has a coupon of 6% and a YTM of 7.82%. You could have typed the numbers into the duration calculator rather than actually calculating the weights and multiplying them by time. To ensure you did the work, please answer this question: What is the present value of the 17th coupon?

Answer 1

$ 15.63

Step-by-step explanation:

The present value of the 17th coupon is the semi-annual coupon discounted at the discount factor that reflect that the payment is the 17th of the 20 coupons payments payable by the bond as done below

semi annual coupon=$1000*6%*6/12=$30

The discount factor applicable is 1/(1+7.82%/2)^17=1/(1+3,91%)^17=0.520984902

The present value of the 17th coupon=coupon amount*discount factor

=$30*0.520984902 =$15.63

The present of the 17th coupon is $ 15.63

This is then applied in bond duration calculation