how to calculate number of days invested in simple interest

To calculate the number of days invested in a simple interest scenario, you can rearrange the formula for simple interest:

\[
I = \frac{P \cdot r \cdot t}{100}
\]

Where:
- $I$ is the simple interest earned,
- $P$ is the principal amount (the initial investment),
- $r$ is the annual interest rate (in percentage),
- $t$ is the time in years (which we will convert to days).

To find the time $t$ in days, we need to rearrange the formula to solve for $t$:

\[
t = \frac{I \cdot 100}{P \cdot r}
\]

Since we want the time in days, and there are 365 days in a year (or 366 in a leap year), we convert the time from years to days:

\[
\text{Number of days} = t \times 365
\]

### Steps:
1. Rearrange the formula to solve for time in years.
2. Multiply the result by 365 to convert it to days.

### Example:
If you invest $1,000 at an annual interest rate of 5% and earn $50 in simple interest, the number of days invested is:

\[
t = \frac{50 \times 100}{1000 \times 5} = 1 \text{ year}
\]

In days:
\[
\text{Number of days} = 1 \times 365 = 365 \text{ days}
\]

Would you like more details on this, or do you have any questions?

### Related Questions:
1. How does the formula change for compound interest?
2. What happens if the interest rate changes periodically?
3. Can the number of days be fractional in this context?
4. How does leap year affect the calculation for days?
5. What is the relationship between interest rates and the number of days?

**Tip:** Always double-check if the interest rate provided is annual, monthly, or daily.

Learn how to calculate the number of days invested in a simple interest scenario using key formulas such as I = (P * r * t) / 100. This guide explains step-by-step how to rearrange the formula to solve for time and convert it into days, using a practical example. Suitable for students in Grades 8-10.

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