what is the future value of $270 invested at 7% simple interest for 82 days? (round your answer to the…

Explanation:

Step1: Recall the simple - interest formula

The formula for simple interest is $A = P(1 + rt)$, where $A$ is the future value, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P=$270$, $r = 0.07$ (since $7%=0.07$), and $t=\frac{82}{365}$ years (assuming a non - leap year with 365 days).

Step2: Substitute the values into the formula

[ \begin{align*} A&=270\left(1+0.07\times\frac{82}{365}\right)\ &=270\left(1+\frac{0.07\times82}{365}\right)\ &=270\left(1+\frac{5.74}{365}\right)\ &=270\left(1 + 0.0157534\right)\ &=270\times1.0157534 \end{align*} ]

Step3: Calculate the value of $A$

[A = 270\times1.0157534=274.253418\approx274.25]

Answer:

$274.25$