Question

A bond trader purchased each of the following bonds at a yield to maturity of 8%. Immediately after she purchased the bonds, interest rates fell to 5%. What is the percentage change in the price of each bond after the decline in interest rates? Assume annual coupons and annual compounding. Fill in the following table. Do not round intermediate calculations. Round your answers to two decimal places

Find for: 30-year zero

Price @ 8%, Price @ 5%, Percentage change

Answer 1

Considering a 30 year 0 coupon bond, please note that the price of the bond will change as the interest rates fall from 8% to 5%. The price will increase as a result of this movement.

Assuming the par value of the bond to be USD 1 million. We calculate the present value of 1 mn to be received at the end of 30 years for both scenarios - 8% YTM and 5% YTM

Price@ 8% = $1000000/(1+8%)^30$ %)^30 = USD 99,377 Answer

Price@ 5% = $1000000/(1+5%)^30$ %)^30 = USD 231,377 Answer