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Sanders Colon
06/23/2023 · Junior High School

Your broker charges you \( 2.5 \% \) commission on the market value of bonds you buy or sell. If you wish to buy a par value \( \$ 1,000 \) bond from Cuyahoga County with a market rate of 86.681 , approximately how much will you owe your broker? a. \( \$ 25.00 \) b. \( \$ 21.67 \) c. \( \$ 89.18 \) d. \( \$ 27.17 \)

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Step-by-step Solution

To calculate the amount you will owe your broker for the commission on the bond purchase, follow these steps: 1. **Determine the market value of the bond**: The market rate is given as 86.681, which means the bond is selling for 86.681% of its par value. The par value of the bond is \( \$ 1,000 \). \[ \text{Market Value} = \text{Par Value} \times \left( \frac{\text{Market Rate}}{100} \right) \] \[ \text{Market Value} = 1000 \times \left( \frac{86.681}{100} \right) = 1000 \times 0.86681 = 866.81 \] 2. **Calculate the broker's commission**: The broker charges a commission of \( 2.5\% \) on the market value of the bond. \[ \text{Commission} = \text{Market Value} \times \left( \frac{2.5}{100} \right) \] \[ \text{Commission} = 866.81 \times 0.025 = 21.67025 \] 3. **Round the commission to two decimal places**: \[ \text{Commission} \approx 21.67 \] Thus, the amount you will owe your broker is approximately \( \$ 21.67 \). The correct answer is **b. \( \$ 21.67 \)**.

Quick Answer

The amount you will owe your broker is approximately \( \$ 21.67 \). Therefore, the correct answer is b. \( \$ 21.67 \).
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