XYZ Corporation invests $11,000 into 91-day treasury bills with an interest rate of 2.7%. If the broker charges a $25 commission, what is the yield?
yield = [?] %
yield = amount invested (interest rate) (days invested / 360 days) / amount invested (days invested / 360 days) + commission
Give your answer as a percent rounded to the nearest hundredth.
Answer (2)
Calculate the interest earned: Interest = 11000 × 0.027 × 360 91 = 74.915 .
Calculate the denominator: Denominator = 11000 × 360 91 + 25 = 2805.555... .
Calculate the yield: Yield = 2805.555... 74.915 = 0.026701... .
Convert to percentage and round: Yield percentage = 0.026701... × 100 ≈ 2.67% . The final answer is 2.67% .
Explanation
Identify Given Values First, let's identify the given values:
Amount invested: $11 , 000 Interest rate: 2.7% = 0.027 Days invested: 91 days Commission: $$25
Calculate Interest Earned Next, we will calculate the interest earned using the formula:
Interest = Amount invested × Interest rate × 360 Days invested
Substituting the values, we get:
Interest = 11000 × 0.027 × 360 91
Interest = 11000 × 0.027 × 0.252777...
Interest = 74.915
Calculate the Denominator Now, we calculate the denominator of the yield formula:
Denominator = Amount invested × 360 Days invested + Commission
Denominator = 11000 × 360 91 + 25
Denominator = 11000 × 0.252777... + 25
Denominator = 2780.555... + 25
Denominator = 2805.555...
Calculate the Yield Now, we calculate the yield using the formula:
Yield = Denominator Interest
Yield = 2805.555... 74.915
Yield = 0.026701...
Convert to Percentage To express the yield as a percentage, we multiply by 100:
Yield percentage = Yield × 100
Yield percentage = 0.026701... × 100
Yield percentage = 2.6701...
Round to Nearest Hundredth Finally, we round the yield percentage to the nearest hundredth:
Yield percentage ≈ 2.67%
Final Answer Therefore, the yield is approximately 2.67% .
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 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 after accounting for all costs.
The yield from an $11,000 investment in 91-day treasury bills with a 2.7% interest rate and a $25 commission is approximately 2.67%. This is calculated by determining the interest earned, the total cost including commission, and then finding the yield as a percentage. After rounding, the final yield percentage is 2.67%.
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