xyz corporation invests $10,000 into 91 - day treasury bills with an interest rate of 2.5%. if the broker…

xyz corporation invests $10,000 into 91 - day treasury bills with an interest rate of 2.5%. if the broker charges a $20 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 $10,000 into 91 - day treasury bills with an interest rate of 2.5%. if the broker charges a $20 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: Calculate the interest earned

The formula for simple - interest is $I = P\times r\times t$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. Here, $P=$10000$, $r = 0.025$, and $t=\frac{91}{360}$ years. $I=10000\times0.025\times\frac{91}{360}=\frac{10000\times0.025\times91}{360}=\frac{22750}{360}\approx63.1944$

Step2: Calculate the yield using the given formula

The yield formula is $yield=\frac{amount\ invested\times(interest\ rate)\times(\frac{days\ invested}{360\ days})}{amount\ invested\times(\frac{days\ invested}{360\ days})+commission}$ Substitute the values: $amount\ invested = 10000$, $interest\ rate=0.025$, $days\ invested = 91$, and $commission = 20$ $yield=\frac{10000\times0.025\times\frac{91}{360}}{10000\times\frac{91}{360}+20}=\frac{63.1944}{ \frac{10000\times91}{360}+20}=\frac{63.1944}{\frac{910000}{360}+20}=\frac{63.1944}{2527.7778 + 20}=\frac{63.1944}{2547.7778}\approx0.0248$

Step3: Convert the yield to a percentage

Multiply the result by 100 to get the percentage. $yield = 0.0248\times100 = 2.48%$

Answer:

$2.48$