If a loan is taken out for 15 900 at 9% and costs 8 586 how long was the loan for

To determine how long the loan was taken out for, we can use the formula for simple interest:

\[
I = P \times r \times t
\]

where:
- \( I \) is the interest paid,
- \( P \) is the principal (initial loan amount),
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time in years.

From the problem, we know:
- \( P = 15,900 \),
- \( r = 9\% = 0.09 \),
- \( I = 8,586 \).

Now, solve for \( t \):

\[
t = \frac{I}{P \times r}
\]

Substituting the given values:

\[
t = \frac{8,586}{15,900 \times 0.09}
\]

Let's calculate this.

The loan was taken out for 6 years.

Would you like more details or have any questions? Here are 5 related questions to expand on this topic:

1. How would the time change if the interest rate were lower?
2. What if the principal amount was higher—how would that affect the duration of the loan?
3. Can we calculate the monthly payments for this loan if it were amortized?
4. How does compound interest affect loan calculations compared to simple interest?
5. What is the difference between nominal and effective interest rates?

**Tip:** Always make sure to convert percentages to decimals (e.g., 9% becomes 0.09) when using them in formulas.

If a loan is taken out for 15,900 at 9% and costs 8,586 how long was the loan for?

Learn how to calculate the time a loan was taken out using the simple interest formula. Given a loan principal of 15,900 at an interest rate of 9%, and an interest cost of 8,586, this problem breaks down the step-by-step process to find the loan duration. Suitable for students in Grades 9-12.

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