Question

The Sonoma Housing Authority is offering $10,000 bonds that

pay 4.2% annual interest. The quoted price of each bond is
$102.125. Ron Kosciusko purchases 15 bonds through a broker
who charges a 1.25% sales commission.
a. What is the cost of the bonds including the commission?
b. What is the total annual interest?
c. What is the annual yield?
d. What is the annual yield if you include the commission as
part of the cost?

Answer 1

The total cost of the bonds including the commission is approximately $1,551.02, the total annual interest is $6,300, the annual yield without the commission is around 4.11%, and the annual yield with the commission is about 4.06%.

Step-by-step explanation:

Calculating the Cost and Yield of Bonds

In order to calculate the cost of the bonds including the commission, first, find the cost before the commission by multiplying the quoted price per bond by the number of bonds:

• Cost before commission = 15 bonds × $102.125 = $1,531.875

Next, calculate the sales commission:

• Sales commission = $1,531.875 × 1.25% = $19.1484375

Adding the sales commission to the initial cost gives us the total cost:

• Total cost including commission = $1,531.875 + $19.1484375 ≈ $1,551.02

For the total annual interest:

• Total annual interest = 15 bonds × $10,000/bond × 4.2% = $6,300

To find the annual yield without considering the commission, we use the formula:

• Annual yield = Total annual interest / (Quoted price × Number of bonds) = $6,300 / $1,531.875 ≈ 0.0411 or 4.11%

When including the commission:

• Annual yield with commission = Total annual interest / Total cost including commission = $6,300 / $1,551.02 ≈ 0.0406 or 4.06%