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To calculate the amount of interest on this loan, we’ll use the **simple interest formula**:

\[
I = P \times r \times \frac{t}{365}
\]

where:
- $ I $ = interest,
- $ P $ = principal amount (initial loan amount),
- $ r $ = annual interest rate,
- $ t $ = time in days,
- and 365 is used because the exact interest method typically assumes a 365-day year.

Given:
- $ P = 4000 $,
- $ r = 0.13 $ (or 13% as a decimal),
- $ t = 160 $ days.

### Step-by-Step Calculation

1. **Convert the interest rate to decimal form:**
   \[
   r = \frac{13}{100} = 0.13
   \]

2. **Substitute the values into the formula:**
   \[
   I = 4000 \times 0.13 \times \frac{160}{365}
   \]

3. **Calculate the interest:**
   \[
   I = 4000 \times 0.13 \times 0.43836 \approx 228.91
   \]

So, the **amount of interest on the loan** is approximately **$228.91**.

Would you like a breakdown of any steps, or have other questions?

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### Related Questions

1. What would the interest be if the loan term was 180 days instead of 160 days?
2. How would the interest amount change if the interest rate was 10% instead of 13%?
3. What is the formula for calculating interest using the "ordinary interest" (360-day year) method?
4. How does compound interest differ from simple interest in loan calculations?
5. If the loan principal were increased to $5,000, what would be the new interest amount for 160 days?

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### Tip
For short-term loans, using the exact interest method (365 days) gives a slightly more accurate result than using the ordinary interest method (360 days).

On May 23, Samantha Best borrowed $4,000 from the Tri City Credit Union at 13% for 160 days. The credit union uses the exact interest method. What was the amount of interest on the loan?

Learn how to calculate the simple interest on a $4,000 loan borrowed at 13% for 160 days using the exact interest method. This problem covers key mathematical concepts, including simple interest calculation, converting percentages, and using time in days. Ideal for students in Grades 9-10.

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