Dijon borrow $900 from a lender that charged simple interest at an annual rate of 7%. When Dijon paid off the loan, he paid $378 in interest. How long was the loan for, in years.
To find out how long the loan was for, we can use the simple interest formula:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
where
- Interest ($I$) is the total interest paid,
- Principal ($P$) is the initial amount borrowed,
- Rate ($r$) is the annual interest rate (in decimal form), and
- Time ($t$) is the time the money is borrowed for in years.
We are given that:
- Interest ($I$) is $378,
- Principal ($P$) is $900, and
- Rate ($r$) is 7% (which is 0.07 in decimal form).
We need to solve for Time ($t$).
Let's plug in the values we have into the formula and solve for $t$:
\[ 378 = 900 \times 0.07 \times t \]
\[ 378 = 63t \]
To find $t$, divide both sides by 63:
\[ t = \frac{378}{63} \]
\[ t = 6 \]
Therefore, the loan was for 6 years.