A bond trader purchased each of the following bonds at a yield to maturity of 7

Question

A bond trader purchased each of the following bonds at a yield to maturity of 7 percent. Immediately after she purchased the bonds, interest rates increased to 7.5 percent. Which is the percentage change in the price of each bond after the increase in interest rates? Which bond is subject to the greatest interest risk rate? Assume a face value of $1,000 for all bonds.

a) 10 year, 9% semi annual coupon

b)30 year, 9% semi annual coupon

c) 5 year, 9% semi annual coupon

If you could please show me your work so I can understand,I have a test on this on Wednesday and have no clue how to do! Thank you so much :)

Explanation / Answer

Price at:
7% YTM / 7.5% YTM / % Change
a) 1,136 / 1,213 / + 6.8
b) 1,226 / 1,374 / + 12.1
c) 1,081 / 1,125 / + 4.1

The longer the term, the greater the risk. (30 yr bonds have the greatest risk)

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