Sure, let's break down the problem step-by-step to find the yield of the investment:
1. Understand the given values:
- The amount invested is \[tex]$8,000.
- The interest rate is 2.1\%.
- The number of days invested is 91 days.
- The commission charged by the broker is \$[/tex]30.
- The number of days in a year for treasury bills is taken as 360 days.
2. Calculate the interest earned:
The interest earned can be calculated using the formula:
[tex]\[
\text{Interest Earned} = \text{Amount Invested} \times \text{Interest Rate} \times \left( \frac{\text{Days Invested}}{\text{Days in a Year}} \right)
\][/tex]
Plugging in the values:
[tex]\[
\text{Interest Earned} = 8000 \times \frac{2.1}{100} \times \left( \frac{91}{360} \right)
\][/tex]
After calculating, the interest earned is:
[tex]\[
\text{Interest Earned} \approx 42.47 \text{ dollars}
\][/tex]
3. Calculate the yield considering the commission:
The yield is calculated by taking the interest earned and adjusting it by the amount invested plus the commission. The formula for the yield is:
[tex]\[
\text{Yield} = \frac{\text{Interest Earned}}{\text{Amount Invested} + \text{Commission}} \times 100\%
\][/tex]
Plugging in the values:
[tex]\[
\text{Yield} = \frac{42.47}{8000 + 30} \times 100\%
\][/tex]
After calculating, the yield is:
[tex]\[
\text{Yield} \approx 0.53\%
\][/tex]
4. Round the yield to the nearest hundredth:
The yield rounded to the nearest hundredth is already given as:
[tex]\[
0.53\%
\][/tex]
So, the yield on the investment, after considering the commission, is approximately 0.53%.
