Question

Suppose in 2018 you buy 3% coupon rate, $100 face value bond for $100 that has 3 years left till

maturity. Suppose in 2019, when interest rates increase to 6%, you decide to sell it.

a) Calculate the selling price of your bond in 2019. How did its value change because of the interest rate

increase?

b) What was your one-year rate of return?

Answer 1

Given,

Bond face value = $100

Yield from bond = 3% * 100 = $3

1 year has passed, 2 years left till maturity

In 2019 interest rates increase to 6%

a) Now, Price of bond = [(Original yield from bond)/(1 + increase in value) + (Face value / (1 + increase in value)]

Hence, present value of Bond = 3/(1+0.06) + 100/(1+0.06)

= 97.17

So the selling price of bond in 2019 due to increase in interest rate = $ 97.17

Change in value = $ (100 - 97.17) = $2.83

b) Rate of Return = [Yield from bond / Face value] + [years left to maturity/face value] = 3/100 + 3/100 = 0.06 = 6%