XYZ Corporation invests $11,000 into 91-day treasury bills with an interest rate of 2.3%. If the broker charges a $20 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]
Answer (2)
Calculate the interest earned: in t eres t = 11000 × 0.023 × 360 91 = 64.15
Calculate the denominator: d e n o mina t or = 11000 t im es 360 91 + 20 = 2800.56
Calculate the yield: y i e l d = 2800.56 64.15 = 0.0229
Convert the yield to percentage: y i e l d _ p erce n t a g e = 0.0229 × 100 = 2.29% 2.29
Explanation
Understanding the Problem Let's break down this problem step by step. We're given an investment in treasury bills, an interest rate, a time period, and a commission fee. Our goal is to calculate the yield percentage using the provided formula.
Calculating the Interest Earned First, we need to calculate the interest earned. The formula for this is: in t eres t = am o u n t _ in v es t e d × in t eres t _ r a t e × 360 d a ys _ in v es t e d Plugging in the values, we get: in t eres t = 11000 × 0.023 × 360 91 in t eres t = 11000 × 0.023 × 0.252777... in t eres t = 64.152777... So, the interest earned is approximately $$64.15.
Calculating the Denominator Next, we calculate the denominator of the yield formula: d e n o mina t or = am o u n t _ in v es t e d × 360 d a ys _ in v es t e d + co mmi ss i o n d e n o mina t or = 11000 × 360 91 + 20 d e n o mina t or = 11000 × 0.252777... + 20 d e n o mina t or = 2780.5555... + 20 d e n o mina t or = 2800.5555... So, the denominator is approximately $2800.56.
Calculating the Yield Now, we can calculate the yield: y i e l d = d e n o mina t or in t eres t y i e l d = 2800.5555... 64.152777... y i e l d = 0.022907...
Converting to Percentage and Rounding Finally, we convert the yield to a percentage: y i e l d _ p erce n t a g e = y i e l d × 100 y i e l d _ p erce n t a g e = 0.022907... × 100 y i e l d _ p erce n t a g e = 2.2907... Rounding to two decimal places, the yield is approximately 2.29% .
Final Answer Therefore, the yield of the treasury bill investment, considering the broker's commission, is approximately 2.29% .
Examples
Treasury bills are often used by corporations to invest excess cash for short periods. For example, XYZ Corporation might have excess cash of $11 , 000 that they don't need for 91 days. Investing in treasury bills allows them to earn a small return. Understanding the yield calculation, including the impact of commissions, helps the company accurately assess the profitability of this short-term investment. This ensures they make informed decisions about managing their finances and maximizing returns on available capital. The yield calculation, as demonstrated, provides a clear picture of the actual percentage return after accounting for all costs.
The yield of XYZ Corporation's investment in treasury bills is approximately 2.29%, calculated by determining the interest earned and factoring in the broker's commission. The steps included calculating interest, the denominator, and then the yield percentage itself. This yield helps in understanding the return on the investment after all costs.
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