Semiannual payment bonds with the same risk (Aaa) and maturity (20 years) as your company's bonds have a simp yield of 9 percent.Your company's treasurer is thinking of issuing at par some $1,000 par value, 20-year, quarterly p bonds.She has asked you to determine what quarterly interest payment, in dollars, the company would have to set i provide the same effective annual rate (EAR) as those on the 20-year, semiannual payment bonds.What would the interest payment be, in dollars?

Question

Quizplus · Accepted Answer

First, we need to find the effective annual rate (EAR) of the semiannual payment bonds with a 9 percent simple yield:
EAR = (1 + 0.09/2)^2 - 1 = 0.0925 or 9.25%

Next, we can use the EAR formula to solve for the quarterly interest payment on the company's bonds:
EAR = (1 + r/4)^4 - 1, where r is the quarterly interest rate
0.0925 = (1 + r/4)^4 - 1
1.0925 = (1 + r/4)^4
Taking the fourth root of both sides, we get:
1.0225 = 1 + r/4
r/4 = 0.0225
r = 0.09 or 9% (same as the semiannual payment bonds)

Finally, we can calculate the quarterly interest payment:
Interest payment = (coupon rate x face value) / number of coupon payments per year
Since the bonds have a 20-year maturity and pay quarterly, there are 80 coupon payments over the life of the bond. To match the EAR of the semiannual payment bonds, the quarterly interest rate is 9% / 4 = 2.25%. Thus, the quarterly interest payment is:
Interest payment = (0.0225 x $1,000) / 4 = $5.625
Therefore, the answer is C) $22.25.

Semiannual Payment Bonds with the Same Risk (Aaa) and Maturity