the principal p is borrowed at simple interest rate r for a period of time t. find the loans future value…

Explanation:

Step1: Convert time to years

Since 1 year has 12 months, $t = 8$ months $=\frac{8}{12}=\frac{2}{3}$ years.

Step2: Use simple - interest formula

The formula for the future value $A$ of a loan with simple interest is $A=P(1 + rt)$, where $P$ is the principal, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P = 3600$, $r=0.065$ (since $6.5%=0.065$), and $t=\frac{2}{3}$. Substitute these values into the formula: [ \begin{align*} A&=3600\left(1+0.065\times\frac{2}{3}\right)\ &=3600\left(1+\frac{0.065\times2}{3}\right)\ &=3600\left(1+\frac{0.13}{3}\right)\ &=3600\times1+3600\times\frac{0.13}{3}\ &=3600 + 1200\times0.13\ &=3600+156\ &=3756 \end{align*} ]

Answer:

$3756$