Karen borrowed $13,000 from Scott at 3.5% for 287 days. Using the exact-days method, how much did Karen pay Scott at the end of the loan?

To calculate how much Karen paid Scott at the end of the loan, we will use the simple interest formula:

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

Where:
- $ I $ = interest amount
- $ P $ = principal (the amount borrowed)
- $ r $ = annual interest rate (in decimal form)
- $ t $ = time in years

### Given:
- $ P = 13,000 $ (the amount borrowed)
- $ r = 3.5\% = 0.035 $
- $ t = \frac{287}{365} $ (since we are using the exact-days method, and there are 365 days in a year)

#### Step 1: Calculate the time in years.
\[
t = \frac{287}{365} = 0.7863 \, \text{years}
\]

#### Step 2: Calculate the interest.
\[
I = 13,000 \times 0.035 \times 0.7863 = 357.26
\]

#### Step 3: Calculate the total amount paid back.
\[
\text{Total amount} = P + I = 13,000 + 357.26 = 13,357.26
\]

### Answer:
Karen paid Scott **$13,357.26** at the end of the loan.

Do you want more details, or do you have any questions?

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Here are five related questions to expand on this topic:
1. How would the interest change if the loan duration was for a leap year (366 days)?
2. What would be the total payment if the interest rate was 4% instead of 3.5%?
3. How would the interest calculation differ if the loan used a 360-day method?
4. What happens if Karen repays the loan early, say after 200 days?
5. How would the interest change if the amount borrowed was $15,000 instead?

**Tip:** When calculating time for loans, always confirm the method used (exact days vs. 360-day year), as it affects the interest.

Learn how to calculate the total payment for a loan of $13,000 at 3.5% interest over 287 days using the exact-days method. This example uses the simple interest formula to find that Karen paid Scott $13,357.26. Suitable for students in Grades 9-12.

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