xyz corporation invests $14,000 into 91 - day treasury bills with an interest rate of 2.2%. if the broker…

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?\nyield = ?%\nyield = \\frac{amount invested(interest rate)(\\frac{days invested}{360 days})}{amount invested(\\frac{days invested}{360 days})+ commission}\ngive your answer as a percent rounded to the nearest hundredth.

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?\nyield = ?%\nyield = \\frac{amount invested(interest rate)(\\frac{days invested}{360 days})}{amount invested(\\frac{days invested}{360 days})+ commission}\ngive your answer as a percent rounded to the nearest hundredth.

Answer

Explanation:

Step1: Identify values

Let the amount invested $P = 14000$, interest rate $r=0.022$, days invested $d = 91$, and commission $C=25$.

Step2: Calculate numerator

The numerator of the yield - formula is $P\times r\times\frac{d}{360}=14000\times0.022\times\frac{91}{360}$. [ \begin{align*} 14000\times0.022\times\frac{91}{360}&=14000\times0.022\times\frac{91}{360}\ &=14000\times\frac{0.022\times91}{360}\ &=14000\times\frac{2.002}{360}\ &=\frac{14000\times2.002}{360}\ &=\frac{28028}{360}\approx77.86 \end{align*} ]

Step3: Calculate denominator

The denominator of the yield - formula is $P\times\frac{d}{360}+C=14000\times\frac{91}{360}+25$. [ \begin{align*} 14000\times\frac{91}{360}+25&=\frac{14000\times91}{360}+25\ &=\frac{1274000}{360}+25\ &\approx3538.89 + 25\ &=3563.89 \end{align*} ]

Step4: Calculate yield

The yield $Y=\frac{\text{numerator}}{\text{denominator}}\times100%$. [ \begin{align*} Y&=\frac{77.86}{3563.89}\times100%\ &\approx0.0219\times100%\ & = 2.19% \end{align*} ]

Answer:

$2.19$