Let's go through the steps to calculate the accrued interest per bond, the total accrued interest, and the total purchase price of the bonds sold by Company 1.
Step 1: Convert the coupon rate to a decimal
- Coupon Rate: 8.75%
- Convert percentage to a decimal: 8.75% = 0.0875
Step 2: Calculate the accrued interest per bond
- Use the formula for accrued interest: [tex]\( \text{Accrued Interest} = \text{Coupon Rate} \times \left( \frac{\text{Days Since Last Interest}}{360} \right) \times 100 \)[/tex]
- Plug in the given values:
[tex]\[
\text{Accrued Interest} = 0.0875 \times \left( \frac{78}{360} \right) \times 100
\][/tex]
[tex]\( \text{Accrued Interest per bond} = 1.90 \)[/tex]
Step 3: Calculate the total accrued interest for all bonds
- Multiply the accrued interest per bond by the number of bonds purchased:
[tex]\[
\text{Total Accrued Interest} = 1.90 \times 15
\][/tex]
[tex]\( \text{Total Accrued Interest} = 28.44 \)[/tex] dollars
Step 4: Calculate the total purchase price
- Add the market price and the commission per bond:
[tex]\[
\text{Cost per bond, including commission} = 102.50 + 3.50 = 106.00
\][/tex]
- Multiply this by the number of bonds purchased:
[tex]\[
\text{Total Market Price with Commission} = 106.00 \times 15 = 1590.00
\][/tex]
- Add the total accrued interest to this amount to get the total purchase price:
[tex]\[
\text{Total Purchase Price} = 1590.00 + 28.44 = 1618.44 \text{ dollars}
\][/tex]
So, the final answers are:
- Accrued Interest per bond: [tex]\( \$1.90 \)[/tex]
- Total Accrued Interest: [tex]\( \$28.44 \)[/tex]
- Total Purchase Price: [tex]\( \$1618.44 \)[/tex]
