The problem involves calculating simple interest using the formula:

$I = P \times r \times t$

Where:

• $I$ is the interest
• $P = 10,500$ is the principal
• $r = 7\% = 0.07$ is the annual interest rate
• $t = \frac{90}{365}$ is the time in years (since 90 days must be converted to years)

Now let's plug in the values:

$t = \frac{90}{365} \approx 0.2466 \text{ years}$

Now calculate the interest:

$I = 10,500 \times 0.07 \times 0.2466$

Let me calculate that for you:

$I \approx 10,500 \times 0.07 \times 0.2466 = 181.74$

So, the simple interest owed is $181.74.

Would you like more details on how this calculation works?

Here are some related questions:

1. What happens if the interest rate increases to 10%?
2. How would the interest change if the loan period was extended to 180 days?
3. What is the formula for compound interest, and how does it differ from simple interest?
4. How would the calculation change if the interest were compounded quarterly instead of being simple interest?
5. Can you calculate the total amount (principal + interest) after the 90-day period?

Tip: When calculating simple interest, always ensure the time is converted to years for consistency.