Question

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 future value is $\square
(simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Recall simple interest formula

The formula for simple interest is $I = Prt$, and the future value $A$ is $A = P + I = P(1 + rt)$. Here, $P$ is principal, $r$ is annual interest rate (in decimal), $t$ is time in years.
First, convert $t = 8$ months to years. Since 1 year = 12 months, $t=\frac{8}{12}=\frac{2}{3}$ years. Convert $r = 6.5\%$ to decimal: $r = 0.065$.

Step2: Calculate interest and future value

Substitute $P = 6000$, $r = 0.065$, $t=\frac{2}{3}$ into the formula $A = P(1 + rt)$.
First, calculate $rt$: $rt=0.065\times\frac{2}{3}=\frac{0.13}{3}\approx0.043333$.
Then, $1 + rt = 1 + 0.043333 = 1.043333$.
Now, $A = 6000\times1.043333\approx6260$.

Answer:

6260