Question

Consider a 10 year bond with face value $1,000, pays 6% coupon semi-annually and has a yield-to-maturity of 7%. How much would the approximate percentage change in the price of bond if interest rate in the economy decreases by 0.80% per year?

(i) Describe and interpret the assumptions related to the problem. (ii) Apply the appropriate mathematical model to solve the problem. (iii) Calculate the correct solution to the problem

Answer 1

The price of the bond before decrease in the interest rate is calculated as follows:-

Semi-annual interest payment = (0.062) x $ 1000

Semi-annual interest payment = $ 30

Bond price before decrease in interest rate = $ 928.94

--------------------------------------------------------------------------------------

The decreased interest rate is calculated as follows

New interest rate = 0.07 - 0.008 x 0.07

New interest rate = 6.94%

The price is calculated at the decreased interest rate

Price after interest rate decrease = $ 933.02

Percentage change in the price of the bond = 0.44%

------------------------------------------------------------------------------------------------------

The following assumptions are made:-

• The coupon rate of the bond remains the same and it continues to make semi-annual payments.
• The maturity duration of the bond remains unchanged.