Loretta Scholten buys nine bonds of Leo Co. 7 ¼ 16 at 103.375. The commission is $3.00 per bond. The current yield to the nearest tenth of a percent is:
7.0%
7.1%
7.2%
7.3%
None of these
To find the current yield, we need to calculate the annual interest income generated by the bonds and divide it by the amount invested.
Let's break down the information given:
- Loretta Scholten buys nine bonds of Leo Co. 7 ¼ 16 at 103.375
- The commission is $3.00 per bond
First, we need to calculate the total cost of purchasing the bonds:
9 bonds at $103.375 each = 9 x $103.375 = $930.375
Next, we need to calculate the total cost including the commission:
Total cost = $930.375 + ($3.00 x 9) = $930.375 + $27.00 = $957.375
Now, let's calculate the annual interest income generated by the bonds:
The bond has an interest rate of 7 ¼ %, which is equivalent to 7.25% or 0.0725 in decimal form.
The bond pays interest semi-annually, so to get the annual interest income, we need to double the semi-annual interest.
Annual interest income = 2 x (0.0725 x $1,000) = 2 x ($72.50) = $145.00
Finally, we can calculate the current yield by dividing the annual interest income by the total cost:
Current yield = ($145.00 / $957.375) x 100 = 0.1513 x 100 ≈ 15.1%
Therefore, the current yield to the nearest tenth of a percent is 15.1%. Since none of the given options match this result, the correct answer is "None of these".
To calculate the current yield, we need to divide the annual interest payment by the purchase price of the bond.
First, we need to calculate the annual interest payment. The bond is a 7 ¼ bond, which means it has a coupon rate of 7.25%.
Now, we need to calculate the dollar amount of interest payment per bond. We can do this by multiplying the coupon rate by the bond's face value.
Let's assume the face value of the bond is $100, so the dollar amount of interest payment per bond is (7.25/100) * 100 = $7.25.
Since Loretta bought 9 bonds, the total annual interest payment is 9 * $7.25 = $65.25.
Now, let's calculate the total cost of the 9 bonds. The price per bond is 103.375, and Loretta bought 9 bonds, so the total cost is 9 * 103.375 = $930.375.
To calculate the current yield, we divide the annual interest payment by the total cost of the bonds and then multiply by 100 to get a percentage.
Current yield = (Annual interest payment / Total cost of bonds) * 100
Current yield = ($65.25 / $930.375) * 100
Current yield ≈ 7.0%
Therefore, the current yield to the nearest tenth of a percent is 7.0%.