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.