Question

lesson 20
finding simple interest continued
5 a new business borrows $320,000 at a yearly simple interest rate of 7%. the total amount the company repays for the loan and interest is $678,400. how long did it take to pay off the loan?

Explanation:

Step1: Recall the simple interest formula

The formula for simple interest is $A = P(1 + rt)$, where $A$ is the total amount repaid, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. First, we need to find the interest amount, then use the simple interest formula $I = Prt$ (where $I$ is the interest) to solve for $t$. The total amount repaid $A$ is the principal plus the interest, so $I = A - P$.

Given $P=\$320,000$, $A = \$678,400$, and $r = 7\%=0.07$.

First, calculate the interest $I$:
$I=A - P=678400 - 320000 = 358400$

Step2: Use the simple interest formula to solve for $t$

We know that $I = Prt$, so we can rearrange the formula to solve for $t$: $t=\frac{I}{Pr}$

Substitute $I = 358400$, $P = 320000$, and $r = 0.07$ into the formula:

$t=\frac{358400}{320000\times0.07}$

First, calculate the denominator: $320000\times0.07 = 22400$

Then, calculate $t$: $t=\frac{358400}{22400}=16$

Answer:

It took 16 years to pay off the loan.