Question

cheryl wants to purchase a par value $500 bond from agram imports. agram imports bonds have a market rate of 102.114 and offer 8.1% interest. if cheryls broker charges a commission of 2.5% of the market value of each bond sold, what is the current yield on cheryls bond?
a. 0.077
b. 0.078
c. 0.081
d. 0.040

Explanation:

Step1: Calculate annual interest

Annual interest = Par value × Interest rate = \( 500 × 0.081 = 40.5 \)

Step2: Calculate market value of bond

Market value = Par value × Market rate (as a decimal) = \( 500 × 1.02114 = 510.57 \)

Step3: Calculate commission

Commission = Market value × Commission rate = \( 510.57 × 0.025 ≈ 12.76425 \)

Step4: Calculate net cost (price paid)

Net cost = Market value + Commission = \( 510.57 + 12.76425 ≈ 523.33425 \)

Step5: Calculate current yield

Current yield = Annual interest / Net cost = \( 40.5 / 523.33425 ≈ 0.077 \)

Answer:

a. 0.077