Question

Rosita purchased a bond for $991.23. She sold the bond for $1,003.42 after 6 months and earned a total return of 5.40% on this investment. Suppose this bond has semiannual interest payments, then what should be the coupon rate of it?

Answer 1

The coupon rate of the bond should be 8.27%.

Step-by-step explanation:

This can be calculated using the following formula:

Total return rate = (Selling price + [(Coupon rate * Face value) / 2] - Purchase price) / Purchase price ............ (1)

Where;

Total return rate = 5.40%, or 0.054

Selling price = $1,003.42

Coupon rate = ?

Bond face value = $1,000

Purchase price = $991.23

Substituting the values into equation (1) and solve for Coupon rate, we have:

0.054 = (1,003.42 + [(Coupon rate * 1,000) / 2] - 991.23) / 991.23

0.054 * 991.23 = 1,003.42 + [(Coupon rate * 1,000) / 2] - 991.23

53.53 - 1,003.42 + 991.23 = (Coupon rate * 1,000) / 2

41.34 * 2 = Coupon rate * 1,000

82.68 = Coupon rate * 1,000

Coupon rate = 82.68 / 1,000

Coupon rate = 0.08268, or 8.268%

Rounding to 2 decimal places, we have:

Coupon rate = 8.27%

Therefore, the coupon rate of the bond should be 8.27%.