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?

He should take the option one of sales commission of 3.1% on
each bond. If he takes the 2nd option, he is required to pay 24$ per
bond. But if he takes the ist option, he is required to pay 15.5$ per bond.
88.754 is the market rate. Total investment is of 500$. Multiply the commission
rate with the amount and you get 15.5 $. There is a difference of 8.5 dollars
between the two options.

Answer Link

Martebi Martebi · Answer 2 · 2022-06-01T10:43:45-04:00

The broker will give Pierce the better deal, and by Broker A’s commission will be $10.24 less than Broker B’s.

What is the deal about?

In the question above, the municipal bond with a par value = $500

To find the market value of the bond, it will be:

= $\frac{88.754}{100}$ x 500

= 443.77

Note that the Commission rate charged by broker A = 3.1%

Therefore, the Commission of broker A will be = $\frac{3.1}{100}$ x 443.77

= $13.757

The Commission of broker B = $24

Note also that the difference between the commission of broker A and broker B will be:

= 24 - 13.756

= $10.24

Therefore, looking at the above, Broker A's commission will be $10.24 and thus it is less then Broker B's.

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