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 over 360 days is $\frac{91}{360}$. So the numerator is $14000\times0.022\times\frac{91}{360}$.

$$
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Step2: Calculate the denominator

Next, we calculate the denominator. The amount invested times $\frac{91}{360}$ plus the commission. The amount invested times $\frac{91}{360}$ is $14000\times\frac{91}{360}\approx14000\times0.252778\approx3538.89$, and then we add the $25 commission, so the denominator is $3538.89 + 25 = 3563.89$.

Step3: Calculate the yield

Now we divide the numerator by the denominator and multiply by 100 to get the yield percentage. So yield is $\frac{77.8656}{3563.89}\times100$.

$$ \frac{77.8656}{3563.89}\times100\approx0.02185\times100 = 2.185\approx2.19 $$

Answer:

2.19%