XYZ Corporation invests $15,000 into 91-day treasury bills with an interest rate of 1.9%. If the broker charges a $20 commission, what is the yield?
$\begin{array}{c}
\text { yield }=[?] % \\
\text { yield }=\frac{\text { amount invested (interest rate) }\left(\frac{\text { days invested }}{360 \text { days }}\right)}{\text { amount invested }\left(\frac{\text { days invested }}{360 \text { days }}\right)+\text { commission }}
\end{array}$
Give your answer as a percent rounded to the nearest hundredth.
Answer (1)
Calculate the interest earned: Interest = 15000 × 0.019 × 360 91 ≈ 71.73 .
Calculate the denominator: Denominator = 15000 × 360 91 + 20 ≈ 3811.67 .
Calculate the yield: Yield = 3811.67 71.73 ≈ 0.0188 .
Convert to percentage and round: Yield percentage = 0.0188 × 100 ≈ 1.88% .
Explanation
Identify Given Information First, let's identify the given information:
Amount invested: $15 , 000
Interest rate: 1.9% = 0.019
Days invested: 91 days
Commission: $$20
Calculate Interest Earned Next, we will calculate the interest earned using the formula:
Interest = Amount invested × Interest rate × 360 Days invested
Substituting the given values:
Interest = 15000 × 0.019 × 360 91
Interest = 15000 × 0.019 × 0.252777...
Interest = 71.729166...
So, the interest earned is approximately $71.73 .
Calculate the Denominator Now, we will calculate the denominator of the yield formula:
Denominator = Amount invested × 360 Days invested + Commission
Substituting the given values:
Denominator = 15000 × 360 91 + 20
Denominator = 15000 × 0.252777... + 20
Denominator = 3791.666... + 20
Denominator = 3811.666...
So, the denominator is approximately 3811.67 .
Calculate the Yield Now, we calculate the yield using the formula:
Yield = Denominator Interest
Substituting the calculated values:
Yield = 3811.666... 71.729166...
Yield = 0.018818...
To express the yield as a percentage, we multiply by 100:
\text{Yield percentage} = 0.018818... \times 100 = 1.8818...\%$ 5. Round to Nearest Hundredth Finally, we round the yield percentage to the nearest hundredth: \text{Yield percentage} \approx 1.88%$
Final Answer Therefore, the yield is approximately 1.88% .
Examples
Understanding treasury bill yields is crucial in finance. For instance, if you're comparing different investment options, knowing the yield helps you assess the actual return after accounting for fees. Imagine you're deciding between two treasury bills: one with a slightly higher interest rate but also higher commission fees. Calculating the yield for each allows you to make an informed decision based on the actual percentage return on your investment, ensuring you choose the most profitable option. This calculation provides a clear, standardized measure for comparing investment opportunities.
