XYZ Corporation invests $5,000 into 91-day treasury bills with an interest rate of 2.5%. If the broker charges a $30 commission, what is the yield?

[tex]
\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}
[/tex]

Give your answer as a percent rounded to the nearest hundredth.

Calculate the interest earned using the formula: I n t eres t = A m o u n t × R a t e × 360 D a ys ​ .
Calculate the denominator using the formula: De n o mina t or = A m o u n t × 360 D a ys ​ + C o mmi ss i o n .
Calculate the yield using the formula: Yi e l d = De n o mina t or I n t eres t ​ .
Convert the yield to a percentage and round to the nearest hundredth: 2.44% ​ .

Explanation

Identify Given Information First, let's identify the given information:


Amount invested: $5 , 000
Interest rate: 2.5% = 0.025
Days invested: 91 days
Commission: $30

We need to calculate the yield using the given formula and round it to the nearest hundredth.

Calculate Interest Earned Next, we calculate the interest earned. The formula for simple interest is:

I n t eres t = A m o u n t × R a t e × T im e
In this case, the time is given in days, so we need to divide by 360 to annualize it:
I n t eres t = 5000 × 0.025 × 360 91 ​

Calculate the Denominator Now, we calculate the denominator of the yield formula:

De n o mina t or = A m o u n t × 360 D a ys ​ + C o mmi ss i o n
De n o mina t or = 5000 × 360 91 ​ + 30

Calculate the Yield Now, we calculate the yield:

Yi e l d = De n o mina t or I n t eres t ​
Yi e l d = 5000 × 360 91 ​ + 30 5000 × 0.025 × 360 91 ​ ​

Calculate Yield Percentage To find the yield as a percentage, we multiply the yield by 100:

Yi e l d _ p erce n t a g e = Yi e l d × 100
Yi e l d _ p erce n t a g e = 5000 × 360 91 ​ + 30 5000 × 0.025 × 360 91 ​ ​ × 100
After performing the calculations, the yield percentage is approximately 2.44% .

Round to Nearest Hundredth Finally, we round the yield percentage to the nearest hundredth, which is 2.44% .

State the Final Answer Therefore, the yield is 2.44% .


Examples
Understanding investment yields is crucial in finance. For instance, if you're comparing different short-term investment options like treasury bills or certificates of deposit, calculating the yield helps you determine which investment provides a better return, especially when commissions or fees are involved. This calculation allows you to make informed decisions about where to allocate your funds to maximize your earnings while considering all associated costs. For example, knowing the yield helps in comparing a T-bill with a slightly lower interest rate but no commission to one with a higher rate but a commission.

Answered by GinnyAnswer | 2025-07-08