https://file.aiquickdraw.com/mathbot/file/1727676064635d8ocnvve.jpg

From the image, you have a financial formula that seems to involve future value (FV), present value (PV), and interest rates.

The general equation appears to be a future value formula:

\[
FV = PV (1 + r)^t
\]

Where:
- **FV** is the future value,
- **PV** is the present value,
- **r** is the interest rate,
- **t** is the number of periods (or time).

The second part of the image shows this equation used with specific numbers:

\[
\frac{2000}{1000} = (1 + r)^t
\]

This equation can be simplified as:

\[
2 = (1 + r)^t
\]

The last part shows a similar format with different values, probably involving another interest rate formula:

\[
\frac{1000}{1000} = (1 + r)
\]

This simplifies to:

\[
1 = 1 + r
\]

This implies \( r = 0 \), meaning there is no interest in this scenario.

### Questions:
1. Would you like me to solve for \( r \) or \( t \) in the first equation?
2. Do you need further clarification on how to manipulate the formulas?
3. Should I explain compound interest more thoroughly?
4. Would you like to use a specific time value (e.g., years or months) for the equation?
5. Are you working on an investment or loan problem that needs these formulas?

**Tip:** The compound interest formula \( FV = PV(1 + r)^t \) assumes that interest is compounded once per period. Be sure to clarify if the compounding frequency changes (e.g., monthly or quarterly), as the formula will need to be adjusted accordingly.

From the image, you have a financial formula that seems to involve future value (FV), present value (PV), and interest rates.

Explore how to calculate future value (FV) using the formula FV = PV(1 + r)^t. Learn how to simplify financial equations involving present value (PV), interest rate (r), and time (t). This problem is suitable for students learning algebraic concepts related to exponential growth and finance, typically in Grades 9-12.

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