Question

(With this problem there is a table). The percent prices are listed atop and across as price at 8% price at 6% and the percentage change. Each of these have their own row and column. An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 8% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell, and each then had a new YTM of 6%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table. Round your answers to the nearest cent or to two decimal places. Enter all amounts as positive numbers. 10-year, 10% annual coupon $ $ % 10-year zero 5-year zero 30-year zero $100 perpetuity

Answer 1

I just used the equation P=sum of(100/(1+y)^t] + 1000/(1+y)^n for the coupon bearing bond, P = 1000/(1+y)^n for the zero coupon bonds, and P = M/y for the perpetuity instrument. A quick calculation yielded the following answers:

Price @ 8% Price @ 6% % Change

10-year, 10% annual coupon $1134.20 $1294.40 14.12%
10Y Zero Coupon $463.19 $558.39 20.55%
5Y Zero Coupon $680.58 $747.26 9.80%
30Y Zero Coupon $99.38 $174.11 75.20%
$100 Perp. $1250.00 $1666.67 33.33%