Answer:
The coupon rate of the bond should be 8.27%.
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%.
