finance homework question Interest Rate Sensitivity

Question

A bond trader purchased each of the following bonds at a yield to maturity of 10%. Immediately after she purchased the bonds, interest rates fell to 7%. What is the percentage change in the price of each bond after the decline in interest rates? Fill in the following table. Round your answers to two decimal places.

                   Price @ 10% /Price @ 7/percentage change

10-year zero %
5-year zero %
30-year zero %
$100 perpetuity %

Answer 1

Assuming par values of $100 and semi-annual compounding, I just used the equation P = 100/(1+y)^n for the zero coupon bonds, and P = M/y for the perpetuity instrument. A quick calculation yielded the following answers:

 

                              Price @ 10% Price @ 7% % Change
10Y Zero Coupon          $37.69        $50.26       33.35%
5Y Zero Coupon           $61.39        $70.89       15.48%
30Y Zero Coupon          $5.35         $12.69       137.10%
$100 Perp.               $1,000.00     $1,428.57     42.86%

 

If your par value is $1,000, just multiply the prices of the bonds by 10.