To calculate the yield of the treasury bill investment, we will use the given formula and input the provided values step by step.
1. Identify the known values:
- Amount invested: \[tex]$5,000
- Interest rate: 2.5% (or 0.025 as a decimal)
- Commission: \$[/tex]30
- Days invested: 91 days
- Total days in a year: 360 days (as per the financial convention for such calculations)
2. Substitute the known values into the 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]
[tex]\[
\text{yield} = \frac{5000 \times 0.025 \times \left(\frac{91}{360}\right)}{5000 \times \left(\frac{91}{360}\right) + 30}
\][/tex]
3. Simplify the expression in the numerator and the denominator:
- Calculate the expression inside the parentheses first:
[tex]\[
\frac{91}{360} \approx 0.25278
\][/tex]
4. Calculate the numerator:
[tex]\[
5000 \times 0.025 \times 0.25278 \approx 31.5975
\][/tex]
5. Calculate the denominator:
[tex]\[
5000 \times 0.25278 + 30 \approx 1263.9 + 30 = 1293.9
\][/tex]
6. Calculate the yield:
[tex]\[
\text{yield} = \frac{31.5975}{1293.9} \approx 0.02443
\][/tex]
7. Convert the yield to a percentage and round to the nearest hundredth:
[tex]\[
0.02443 \times 100 \approx 2.44\%
\][/tex]
Therefore, the yield of the \[tex]$5,000 investment in the 91-day treasury bills with an interest rate of 2.5% and a \$[/tex]30 commission is 2.44%.
