What principal will earn $55.99 interest at 9.75% p.a. from February 4, 2021, to July 6, 2021?

To calculate the principal that will earn $55.99 interest at an annual interest rate of 9.75% from February 4, 2021, to July 6, 2021, we first need to determine the number of days between these two dates.

### Step 1: Calculate the number of days
- From February 4, 2021, to July 6, 2021, we calculate the days as follows:
  - February 4 to February 28: 24 days (since 2021 is not a leap year)
  - March: 31 days
  - April: 30 days
  - May: 31 days
  - June: 30 days
  - July 1 to July 6: 6 days

Adding these up:
\[
24 + 31 + 30 + 31 + 30 + 6 = 152 \text{ days}
\]

### Step 2: Use the simple interest formula
Given:
- Interest = $55.99
- Rate = 9.75% per annum, or 0.0975 as a decimal
- Time = $ \frac{152}{365} $ years

Using the formula:
\[
\text{Principal} = \frac{\text{Interest}}{\text{Rate} \times \text{Time}}
\]

Substituting the values:
\[
\text{Principal} = \frac{55.99}{0.0975 \times \frac{152}{365}} 
\]

Let's calculate this:

\[
\text{Principal} = \frac{55.99}{0.0975 \times 0.41644} = \frac{55.99}{0.0405979} \approx 1379.09
\]

So, the principal is approximately **$1,379.09**.

Would you like any further details or have any questions?

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Here are 8 related questions that expand on this topic:
1. How would the principal change if the interest rate were 8.5% instead of 9.75%?
2. What is the interest earned if the principal were $2,000 at the same interest rate and time period?
3. How does the calculation differ if the interest is compounded monthly instead of being simple interest?
4. Can you calculate the interest earned if the time period were extended by 30 days?
5. What would the principal be if the interest earned were $75.00 under the same conditions?
6. How does changing the number of days affect the principal required for a given interest?
7. What is the formula for finding the time required to reach a specific interest amount given the principal and rate?
8. How would the principal required change if the interest rate were compounded quarterly?

**Tip:** Always be precise in counting days between dates, especially in non-leap and leap years, to ensure accurate interest calculations.

Learn how to calculate the principal that will earn $55.99 interest at an annual interest rate of 9.75% from February 4, 2021, to July 6, 2021. Step-by-step solution using the simple interest formula. Suitable for high school students.

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