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.