Question

An investor bought a 20-year bond at par with a semiannual coupon and a 3% yield-to-maturity. One year later, due to a decline in interest rates, she sold the bond at a 2% yield to maturity. What was her capital gain or loss?

15.7%

8.6%

18.7%

16.4%

14.3%

Answer 1

The initial bond was purchased at par

P0 = $1,000

Par bonds will have coupon rate equal to yield to maturity

Coupon rate = 3%

cpn = 1,000 * 0.03/2 = 15

Now the yield to maturity is 2%

r = 2%/2 = 0.01

n = 19 * 2 = 38

Gain = Selling price/Purchase price - 1

Gain = 1,157.4233164515/1,000 - 1

Gain = 0.1574233165

Gain = 15.7%