To determine the yield of the investment, we need to follow the formula:
[tex]\[\text{yield} = \frac{\text{interest earned}}{\text{amount invested + commission}} \times 100\%\][/tex]
Given the following information:
- Amount invested ([tex]\( P \)[/tex]) = [tex]$13,000
- Interest rate (\( r \)) = 1.8% or 0.018
- Days invested (\( t \)) = 91
- Total days in a year = 360
- Commission = $[/tex]20
Let's break down the steps to find the yield.
### Step 1: Calculate the Interest Earned
First, we calculate the interest earned over the 91 days:
[tex]\[
\text{Interest earned} = \text{amount invested} \times \text{interest rate} \times \left(\frac{\text{days invested}}{\text{total days in year}}\right)
\][/tex]
Substituting the given values:
[tex]\[
\text{Interest earned} = 13000 \times 0.018 \times \left(\frac{91}{360}\right)
\][/tex]
### Step 2: Simplify the Equation to Find the Interest Earned
[tex]\[
\text{Interest earned} = 13000 \times 0.018 \times 0.25278
\][/tex]
[tex]\[
\text{Interest earned} = 59.15
\][/tex]
### Step 3: Calculate the Yield Percentage
Now, we calculate the yield percentage by dividing the interest earned by the total amount invested plus the commission, and then multiplying by 100 to get the percentage.
[tex]\[
\text{yield} = \frac{\text{Interest earned}}{\text{Amount invested} + \text{Commission}} \times 100\%
\][/tex]
Substituting the values:
[tex]\[
\text{yield} = \frac{59.15}{13000 + 20} \times 100\%
\][/tex]
### Step 4: Simplify the Equation to Find the Yield Percentage
[tex]\[
\text{yield} = \frac{59.15}{13020} \times 100\%
\][/tex]
[tex]\[
\text{yield} \approx 0.4543\%
\][/tex]
Thus, the interest earned is approximately $59.15 and the yield is approximately [tex]\(0.4543\%\)[/tex].
