Question

Suppose in 2020 you buy 2% coupon rate, $1000 face value bond for $1000 that has 3 years left till maturity. Suppose in 2021, when interest rates increase to 5%, you decide to sell it. a) Calculate the selling price of your bond in 2021. How did its value change because of the interest rate increase?

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

Answer 1

a) Value of the bond in 2021 = 20/1.05 + 20/1.05^2 + 1000/1.05^2 = 19.05 + 18.14 + 907.03 = 944.22

So the selling price of the bond in 2021 will be 944.22. The selling price has decreased because of increase in interest rates. Since the interest rates has increased to 5%, so a $1000 deposit will yield $50 instead of $20 from the bond. So the bond is less attractive now. As a result the price of the bond has gone down.

b) Coupon Payment from the bond in 2021 = 2% of 1000 = $20

Selling Price of the bond = $944.22

Total Income from the Bond = $20 + $944.22 = $964.22

Buying Price of the bond = $1000

Return from the bond = 964.22/1000 - 1 = -3.58%

So the one year return from the bond is -3.58%.

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