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

the principal p is borrowed at simple - interest rate r for a period of time t. find the loans future value, a, or the total amount due at time t. p = $6000, r = 6.5%, t = 8 months

the principal p is borrowed at simple - interest rate r for a period of time t. find the loans future value, a, or the total amount due at time t. p = $6000, r = 6.5%, t = 8 months

Answer

Explanation:

Step1: Convert rate to decimal and time to years

The interest rate $r = 6.5%=0.065$. The time $t = 8$ months. Since there are 12 months in a year, $t=\frac{8}{12}=\frac{2}{3}$ years.

Step2: Use the simple - interest formula for future value

The formula for the future value $A$ of a loan with simple interest is $A=P(1 + rt)$. Substitute $P = 6000$, $r=0.065$, and $t=\frac{2}{3}$ into the formula. [ \begin{align*} A&=6000\left(1+0.065\times\frac{2}{3}\right)\ &=6000\left(1+\frac{0.13}{3}\right)\ &=6000\times\left(\frac{3 + 0.13}{3}\right)\ &=2000\times3.13\ &=6260 \end{align*} ]

Answer:

$6260$