Pierce wishes to purchase a municipal bond with a par value of \( \$ 500 \) from Chattahoochee County, and he is trying to decide which broker he should employ to purchase the bond. Broker \( A \) charges a \( 3.1 \% \) commission on the market value of each bond sold. Broker B charges a flat \( \$ 24 \) for each bond sold. If the bond has a market rate of 88.754 , which broker will give Pierce the better deal, and by how much? a. Broker B's commission will be \( \$ 9.75 \) less than Broker A's. b. Broker B's commission will be \( \$ 3.51 \) less than Broker A's. c. Broker A's commission will be \( \$ 13.76 \) less than Broker B's. d. Broker A's commission will be \( \$ 10.24 \) less than Broker B's.

To determine which broker will give Pierce the better deal, we need to calculate the commission for each broker based on the market value of the bond. Given: - Par value of the bond = $500 - Market rate of the bond = 88.754 - Broker A charges a 3.1% commission on the market value of each bond sold - Broker B charges a flat $24 for each bond sold Let's calculate the commission for each broker: 1. Commission for Broker A: Commission = 3.1% of Market Value Commission = 0.031 * 88.754 * 500 2. Commission for Broker B: Commission = Flat Rate Commission = $24 Now, we will compare the commissions of Broker A and Broker B to determine which broker will give Pierce the better deal. Calculate the value by following steps: - step0: Calculate: \(0.031\times 88.754\times 500\) - step1: Multiply the terms: \(2.751374\times 500\) - step2: Multiply the numbers: \(1375.687\) The commission for Broker A is $1375.687. Now, let's compare the commissions of Broker A and Broker B to determine which broker will give Pierce the better deal. Calculate the value by following steps: - step0: Calculate: \(1375.687-24\) - step1: Subtract the numbers: \(1351.687\) The commission for Broker A is $1351.687. Comparing the commissions: - Broker A's commission is $1351.687 - Broker B's commission is $24 Therefore, Broker A's commission is $1351.687, which is $1337.687 more than Broker B's commission. So, the correct answer is: c. Broker A's commission will be $13.76 less than Broker B's.