𝐴 2

The equation you've provided is:

$A_2 = (A_1 + 20,000) \times (1.04)^8$

This can be interpreted as an exponential growth or compound interest formula, where:

• $A_2$ represents the final amount.
• $A_1$ represents the initial amount.
• $20,000$ is an added value or increment.
• $1.04$ is the growth factor.
• $8$ is the number of periods (perhaps years, months, etc.).

To solve for $A_2$, you need to know the value of $A_1$. Once $A_1$ is known, you can substitute and compute the final value for $A_2$.

Example Calculation (assuming $A_1 = 50,000$):

$A_2 = (50,000 + 20,000) \times (1.04)^8$ First, sum the values inside the parentheses:

$A_2 = 70,000 \times (1.04)^8$ Now calculate $(1.04)^8$:

$(1.04)^8 \approx 1.368569$

Finally:

$A_2 \approx 70,000 \times 1.368569 = 95,800.43$

So, $A_2 \approx 95,800.43$.

Would you like to provide the value of $A_1$, or do you have any other questions?

Related Questions:

1. What is the interpretation of $A_1$ in real-world problems like investment?
2. How does changing the growth factor (1.04) impact the final result?
3. What if the number of periods ($8$) were different, say 5 or 10?
4. How can this formula be used for financial planning, like retirement?
5. Can we derive the formula for continuous compounding?

Tip:

When working with exponential growth, small changes in the growth rate or time period can lead to significant changes in the result.