What principal will earn $ 40.12
 
interest from October 15 comma 2017
​, 
to June 12 comma 2018
​, 
at 9.25
​%?

To solve this problem, we can use the **simple interest formula**:

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

Where:
- $ I $ is the interest earned ($40.12),
- $ P $ is the principal amount (the unknown we are trying to find),
- $ r $ is the annual interest rate (9.25% or 0.0925),
- $ t $ is the time in years.

### Step 1: Determine the time period $ t $ in years
From October 15, 2017, to June 12, 2018:
- From October 15, 2017, to December 31, 2017: $ 31 - 15 = 16 $ days in October, plus 30 days in November, plus 31 days in December = 77 days.
- From January 1, 2018, to June 12, 2018: January (31), February (28), March (31), April (30), May (31), and June 12 days = 163 days.

Total days = 77 days (2017) + 163 days (2018) = 240 days.

Convert to years: 
\[
t = \frac{240}{365} \approx 0.6575 \, \text{years}.
\]

### Step 2: Solve for the principal $ P $
Rearranging the simple interest formula to solve for $ P $:

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

Substitute the known values:

\[
P = \frac{40.12}{0.0925 \times 0.6575}
\]

Let's calculate $ P $.The principal amount that will earn $40.12 in interest from October 15, 2017, to June 12, 2018, at a 9.25% interest rate is approximately **$659.63**.

Would you like more details on any part of the calculation or further clarification?

Here are some related questions:
1. How would the principal change if the interest rate were lower?
2. What if the time period were exactly one year?
3. How do compound interest and simple interest differ in calculation?
4. How would the calculation change if you earned interest monthly instead of daily?
5. What is the impact of different interest compounding frequencies on earnings?

**Tip:** Always convert time periods into years when using the simple interest formula.

What principal will earn $40.12 interest from October 15, 2017, to June 12, 2018, at 9.25%?

Find the principal amount that earns $40.12 in interest from October 15, 2017, to June 12, 2018, at a 9.25% interest rate. This solution uses the simple interest formula and time conversion techniques, suitable for students in Grades 9-11.

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