If a loan is taken out for P15,900 at 9% and cost P8,586. How long was the loan for?

We can solve this using the formula for **simple interest**:

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

where:
- \(I\) is the interest (which we can find by subtracting the principal from the total cost),
- \(P\) is the principal amount (P15,900),
- \(r\) is the annual interest rate (9% or 0.09),
- \(t\) is the time in years, which we need to determine.

### Step 1: Find the Interest \(I\)
Since the total cost of the loan is P8,586, and the principal is P15,900, the interest can be calculated as:

\[
I = 8,586 - 15,900 = -7,314
\]

Since this result is negative, it seems we need clarification or adjustment on the problem's context. Could you confirm if P8,586 is meant to be interest or total repayment?

Let me know if you'd like further details, or if you'd like me to adjust the calculations based on new information.

Here are five questions that can help clarify or expand on the topic:
1. Is P8,586 the total interest, the repayment, or some other cost?
2. Should we use compound interest instead of simple interest?
3. What is the duration of the loan in months instead of years?
4. Were any additional fees or amounts involved in the loan?
5. Can we assume the interest is applied annually?

Tip: Always make sure to distinguish between interest and total cost when solving loan-related problems.

Learn how to calculate the duration of a loan using the simple interest formula. In this problem, a loan of P15,900 is taken at a 9% annual interest rate, and the total cost is P8,586. Discover how to determine the time for repayment with step-by-step guidance, suitable for Grades 9-12.

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