To determine the yield on the investment made by XYZ Corporation, we will use the given yield formula:
[tex]\[
\text{yield} = \frac{\text{amount invested} \times \text{interest rate} \times \left(\frac{\text{days invested}}{360 \text{ days}}\right)}{\text{amount invested} \times \left(\frac{\text{days invested}}{360 \text{ days}}\right) + \text{commission}}
\][/tex]
Let’s break down the problem step-by-step:
1. Identify the given values:
- Investment Amount: [tex]\( \text{amount invested} = \$10,000 \)[/tex]
- Interest Rate: [tex]\( \text{interest rate} = 1.5\% = 0.015 \)[/tex]
- Days Invested: [tex]\( \text{days invested} = 91 \text{ days} \)[/tex]
- Commission: [tex]\( \text{commission} = \$30 \)[/tex]
- Days in a Year (financial convention): [tex]\( 360 \text{ days} \)[/tex]
2. Calculate the numerator of the yield formula:
[tex]\[
\text{yield numerator} = \text{amount invested} \times \text{interest rate} \times \left(\frac{\text{days invested}}{360 \text{ days}}\right)
\][/tex]
[tex]\[
\text{yield numerator} = 10000 \times 0.015 \times \left(\frac{91}{360}\right)
\][/tex]
[tex]\[
\text{yield numerator} = 10000 \times 0.015 \times 0.2527777777777778
\][/tex]
[tex]\[
\text{yield numerator} \approx 37.92
\][/tex]
3. Calculate the denominator of the yield formula:
[tex]\[
\text{yield denominator} = \text{amount invested} \times \left(\frac{\text{days invested}}{360}\right) + \text{commission}
\][/tex]
[tex]\[
\text{yield denominator} = 10000 \times \left(\frac{91}{360}\right) + 30
\][/tex]
[tex]\[
\text{yield denominator} = 10000 \times 0.2527777777777778 + 30
\][/tex]
[tex]\[
\text{yield denominator} \approx 2557.78
\][/tex]
4. Calculate the yield:
[tex]\[
\text{yield} = \frac{\text{yield numerator}}{\text{yield denominator}} \times 100
\][/tex]
[tex]\[
\text{yield} = \frac{37.92}{2557.78} \times 100
\][/tex]
[tex]\[
\text{yield} \approx 1.48\%
\][/tex]
So, the yield on the investment is approximately [tex]\( 1.48\% \)[/tex] when rounded to the nearest hundredth percent.
