Question

xyz corporation invests $14,000 into 91 - day treasury bills with an interest rate of 2.2%. if the broker charges a $25 commission, what is the yield?
yield = ?%
yield = \frac{\text{amount invested}(\text{interest rate})\left(\frac{\text{days invested}}{360\text{ days}}\
ight)}{\text{amount invested}\left(\frac{\text{days invested}}{360\text{ days}}\
ight) + \text{commission}}
give your answer as a percent rounded to the nearest hundredth.

Explanation:

Step1: Calculate the numerator

First, we calculate the numerator part of the yield formula. The amount invested is $14,000, the interest rate is 2.2% (or 0.022 in decimal), and the days invested is 91. So we have:
\(14000\times0.022\times\frac{91}{360}\)
First, calculate \(14000\times0.022 = 308\). Then, calculate \(308\times\frac{91}{360}\approx308\times0.252778\approx77.8556\)

Step2: Calculate the denominator

Next, calculate the denominator. The amount invested times \(\frac{days\ invested}{360\ days}\) plus the commission. We already know \(14000\times\frac{91}{360}\approx14000\times0.252778\approx3538.89\). Then add the commission of $25: \(3538.89 + 25 = 3563.89\)

Step3: Calculate the yield

Now, divide the numerator by the denominator to get the yield: \(\frac{77.8556}{3563.89}\approx0.02184\). To convert this to a percentage, multiply by 100: \(0.02184\times100 = 2.184\%\), rounded to the nearest hundredth is \(2.18\%\)

Answer:

\(2.18\)