A print shop borrows $9,200 from a credit union for 214 days. The credit union charges simple interest at an annual rate of 5.75% for this loan. Assume each day is one 365th of a year. Find the interest that will be owed after 214 days. And assuming the print shop doesn't make any payments, find the amount owed after 214 days.

To calculate the interest owed after 214 days, we can use the formula for simple interest:

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

Where:
- $I$ is the interest,
- $P$ is the principal (amount borrowed),
- $r$ is the annual interest rate (as a decimal),
- $t$ is the time the money is borrowed (in years).

### Step 1: Convert the given information into the formula.

- $P = 9200$ (the principal),
- $r = 5.75\% = \frac{5.75}{100} = 0.0575$,
- $t = \frac{214}{365}$ (since 214 days is a fraction of a year).

### Step 2: Calculate the interest owed.

Now, substitute these values into the formula:

\[
I = 9200 \times 0.0575 \times \frac{214}{365}
\]

Let me calculate that for you.

It seems there was an issue with the calculation. Let me try that again manually.

\[
I = 9200 \times 0.0575 \times \frac{214}{365}
\]

First, calculate $ \frac{214}{365} $:

\[
\frac{214}{365} \approx 0.5863
\]

Now calculate the interest:

\[
I = 9200 \times 0.0575 \times 0.5863 \approx 9200 \times 0.0337 \approx 310.22
\]

So, the interest owed after 214 days is approximately **$310.22**.

### Step 3: Calculate the total amount owed after 214 days.

The total amount owed is the principal plus the interest:

\[
\text{Total Amount} = P + I = 9200 + 310.22 = 9510.22
\]

Thus, the total amount owed after 214 days is **$9,510.22**.

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Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How would the interest change if the loan was for a full year instead of 214 days?
2. What is the difference between simple and compound interest for this scenario?
3. How can you calculate the monthly interest for a loan with the same conditions?
4. What happens to the total owed if the interest rate changes to 6%?
5. How is the daily interest rate derived from the annual interest rate?

**Tip:** Simple interest is directly proportional to the time borrowed, so the interest grows linearly over time.

Learn how to calculate the simple interest on a $9,200 loan over 214 days at an annual interest rate of 5.75%. This problem involves key concepts such as time conversion, proportional reasoning, and the simple interest formula. Suitable for students in Grades 9-10.

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