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?
[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.
Answer (1)
Calculate the interest earned: in t eres t = 15000 × 0.019 × 360 91 = 71.729166...
Calculate the denominator: d e n o mina t or = 15000 × 360 91 + 20 = 3811.666...
Calculate the yield: y i e l d = 3811.666... 71.729166... = 0.018818...
Convert to percentage and round: y i e l d p erce n t a g e = 0.018818... × 100 ≈ 1.89 1.89 %
Explanation
Understanding the Problem We are given an investment scenario and asked to calculate the yield as a percentage, rounded to the nearest hundredth. The formula for yield is provided, and we have all the necessary values: amount invested, interest rate, days invested, and commission.
Calculating the Interest First, we need to calculate the interest earned using the formula: 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 Substituting the given values: in t eres t = 15000 × 0.019 × 360 91 in t eres t = 15000 × 0.019 × 0.252777... in t eres t = 71.729166...
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 Substituting the given values: d e n o mina t or = 15000 × 360 91 + 20 d e n o mina t or = 15000 × 0.252777... + 20 d e n o mina t or = 3791.666... + 20 d e n o mina t or = 3811.666...
Calculating the Yield Now, we calculate the yield: y i e l d = d e n o mina t or in t eres t y i e l d = 3811.666... 71.729166... y i e l d = 0.018818...
Converting to Percentage To express the yield as a percentage, we multiply by 100: 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 = 0.018818... × 100 y i e l d p erce n t a g e = 1.8818...
Rounding the Result Finally, we round the yield percentage to the nearest hundredth: y i e l d p erce n t a g e ≈ 1.89 Therefore, the yield is approximately 1.89% .
Examples
Treasury bills are a common investment for individuals and corporations looking for a low-risk way to earn a return on their cash. Understanding how to calculate the yield on a treasury bill, taking into account broker commissions, is essential for making informed investment decisions. For example, a company might invest in treasury bills to manage its short-term cash flow, and accurately calculating the yield helps them compare this investment option with other alternatives, such as keeping the cash in a savings account or making other short-term investments. This calculation provides a clear picture of the actual return on investment after accounting for all costs.
