Semi-annual payment bonds with the same risk (Aaa) and maturity (20 years) as your company's bonds have a simple (not EAR) yield of 9 percent.Your company's treasurer is thinking of issuing at par some R1,000 par value, 20-year, quarterly payment bonds.She has asked you to determine what quarterly interest payment, in rands, the company would have to set in order to provide the same effective annual rate (EAR) as those on the 20-year, semi-annual payment bonds.What would the quarterly interest payment be, in rands?

Question

Quizplus · Accepted Answer

The semi-annual yield is 9%, so the effective annual rate (EAR) can be calculated as:
EAR = (1 + 0.09/2)^2 - 1
EAR = 0.0941 or 9.41%
Since the treasurer wants to issue quarterly payment bonds, we need to find the quarterly interest payment that will result in an EAR of 9.41%. Let x be the quarterly payment:
EAR = (1 + x)^4 - 1
0.0941 = (1 + x)^4 - 1
1.0941 = (1 + x)^4
1 + x = (1.0941)^(1/4)
1 + x = 1.0225
x = 0.0225 or 2.25%
Therefore, the quarterly interest payment in rands would be:
R1,000 × 0.0225 = R22.25
Hence, the correct answer is C.

Semi-Annual Payment Bonds with the Same Risk (Aaa) and Maturity