Question

Suppose that you just bought a four-year $1,000 coupon bond with a coupon rate of 5.4% when the market interest rate is 5.4%. One year later, the market interest rate falls to 3.4%.

The rate of return earned on the bond during the year was _%

Answer 1

Face value = 1000

Coupon rate = 5.4%

Coupon payment = 5.4% * 1000 = 54

original term = 4 yrs

Interest rate falls to 3.4% after 1 year

Present value of bond after 1 year when interest rates falls to 3.4%, three years left to maturity

= 54/(1.034) + 54/(1.034^2) + (1000 + 54)/(1.034^3)

= 52.224 + 50.507 + 953.408

= 1056.139

We have received one coupon payment of 54 in previous year

rate of return = {(price after 1 year + coupon amount received in previous year - investment) /investment }

= (1056.139 +64 -1000)/1000

=110.139/1000 = 0.110139

= 11.014%