xyz corporation invests $3,000 into 91 - day treasury bills with an interest rate of 2.9%. if the broker…

xyz corporation invests $3,000 into 91 - day treasury bills with an interest rate of 2.9%. if the broker charges a $30 commission, what is the yield? yield = ?% yield = amount invested(interest rate)(days invested / 360 days) / amount invested(days invested / 360 days) + commission

xyz corporation invests $3,000 into 91 - day treasury bills with an interest rate of 2.9%. if the broker charges a $30 commission, what is the yield? yield = ?% yield = amount invested(interest rate)(days invested / 360 days) / amount invested(days invested / 360 days) + commission

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=$3000$, $r = 0.029$, and $t=\frac{91}{360}$. $I=3000\times0.029\times\frac{91}{360}$ $I = 3000\times0.029\times0.252778\approx22.09$

Step2: Calculate the yield

The yield formula is $yield=\frac{I}{P\times\frac{91}{360}+30}$ Substitute $I = 22.09$, $P = 3000$ into the formula: $yield=\frac{22.09}{3000\times\frac{91}{360}+30}$ $yield=\frac{22.09}{3000\times0.252778 + 30}$ $yield=\frac{22.09}{758.334+30}$ $yield=\frac{22.09}{788.334}\approx0.028$ To convert to a percentage, multiply by 100. $yield = 2.8%$

Answer:

$2.8$