To determine the yield of XYZ Corporation's investment, we need to follow these detailed steps:
1. Assign and identify given values:
- Amount invested ([tex]$P$[/tex]): \[tex]$8,000
- Interest rate ($[/tex]r[tex]$): 2.1% (or 0.021 in decimal form)
- Days invested ($[/tex]t[tex]$): 91 days
- Broker's commission: \$[/tex]30
- Days in a year ([tex]$T$[/tex]): 360 days (as per traditional financial calculations)
2. Calculate the interest earned:
The interest earned ([tex]$I$[/tex]) can be calculated using the formula for simple interest:
[tex]\[
I = P \times r \times \left(\frac{t}{T}\right)
\][/tex]
Substituting in the given values:
[tex]\[
I = 8000 \times 0.021 \times \left(\frac{91}{360}\right)
\][/tex]
This yields:
[tex]\[
I \approx 42.47
\][/tex]
3. Calculate the total return:
The total return is the interest earned minus the broker's commission:
[tex]\[
\text{Total Return} = I - \text{Commission}
\][/tex]
Substituting in our values:
[tex]\[
\text{Total Return} \approx 42.47 - 30 = 12.47
\][/tex]
4. Calculate the yield percentage:
The yield percentage is calculated using the following formula:
[tex]\[
\text{Yield Percentage} = \left(\frac{\text{Total Return}}{P}\right) \times 100
\][/tex]
Substituting in our values:
[tex]\[
\text{Yield Percentage} \approx \left(\frac{12.47}{8000}\right) \times 100 \approx 0.16\%
\][/tex]
Therefore, the yield of XYZ Corporation's investment, rounded to the nearest hundredth, is:
[tex]\[
\boxed{0.16\%}
\][/tex]
