Final answer:
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%