XYZ Corporation invests $5,000 into 91-day treasury bills with an interest rate of 1.5%. If the broker charges a $25 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: in t eres t = 5000 × 0.015 × 360 91 = 18.958333...
Calculate the denominator: d e n o mina t or = 5000 × 360 91 + 25 = 1288.8888...
Calculate the yield: y i e l d = 1288.8888... 18.958333... = 0.014708...
Convert the yield to percentage and round: y i e l d ≈ 1.47% . The final answer is 1.47 % .
Explanation
Identify Given Information First, let's identify the given information:
Amount invested: $5 , 000 Interest rate: 1.5% = 0.015 Days invested: 91 days Commission: $$25
Apply the Formula Next, we'll use the formula provided to calculate the yield:
yield = amount invested × 360 days invested + commission amount invested × interest rate × 360 days invested
Plugging in the values, we get:
yield = 5000 × 360 91 + 25 5000 × 0.015 × 360 91
Calculate Numerator and Denominator Now, let's calculate the numerator:
5000 × 0.015 × 360 91 = 75 × 360 91 = 360 6825 = 18.958333...
And the denominator:
5000 × 360 91 + 25 = 360 455000 + 25 = 1263.8888... + 25 = 1288.8888...
Calculate the Yield Now, we divide the numerator by the denominator:
yield = 1288.8888... 18.958333... = 0.014708...
Convert to Percentage and Round To express the yield as a percentage, we multiply by 100:
0.014708... × 100 = 1.4708...
Finally, we round the yield percentage to the nearest hundredth:
1.4708... ≈ 1.47%
Final Answer Therefore, the yield is approximately 1.47% .
Examples
Treasury bills are a common investment for individuals and corporations. Understanding the yield, which represents the return on investment, is crucial for making informed financial decisions. For example, if a company invests in treasury bills to manage its short-term cash, knowing the yield helps them compare it to other short-term investment options like certificates of deposit or money market accounts. This calculation ensures they are maximizing their returns while maintaining liquidity.
