Semiannual payment bonds with the same risk (Aaa)and maturity (20 years)as your company's bonds have a simple (not effective annual rate)yield of 9 percent.Your company's treasurer is thinking of issuing at par some $1,000 par value,20-year,quarterly payment bonds.She has asked you to determine what quarterly interest payment,in dollars,the company would have to set in order to provide the same effective annual rate (EAR)as those on the 20-year,semiannual payment bonds.What would the quarterly interest payment be,in dollars?
A) $45.00
B) $25.00
C) $22.25
D) $27.50
E) $23.00

Question

Quizplus · Accepted Answer

First, we need to convert the semiannual yield of 9% to an effective annual rate (EAR):

EAR = (1 + 0.09/2)^2 - 1
EAR = 0.0925 or 9.25%

Next, we need to find the quarterly interest payment that would provide the same EAR for the quarterly payment bonds:

EAR = (1 + R/4)^4 - 1
0.0925 = (1 + R/4)^4 - 1
1.0925 = (1 + R/4)^4
(1 + R/4) = 1.0225^(1/4)
(1 + R/4) = 1.0220
R = 0.0220 or 2.20%

The quarterly interest payment can now be calculated using the bond's par value:

PMT = (R/4) x $1,000
PMT = (0.0220/4) x $1,000
PMT = $5.50

Therefore, the quarterly interest payment would be $5.50, which is option C.

Semiannual Payment Bonds with the Same Risk (Aaa)and Maturity (20