This is a compound interest problem, and we can calculate the future value using the compound interest formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (initial deposit).
• $r$ is the annual interest rate (in decimal form).
• $n$ is the number of times the interest is compounded per year.
• $t$ is the time in years.

Given:

• $P = 8000$
• $r = 18\% = 0.18$
• $n = 1$ (compounded annually)
• $t$ is the variable (duration in years).

Part 1: General Formula Without Rounding

Plugging the given values into the formula:

$A = 8000 \left(1 + \frac{0.18}{1}\right)^{1 \cdot t}$

$A = 8000 \left(1.18\right)^t$

This is the general expression for the account balance $A$ after $t$ years.

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If you'd like me to evaluate $A$ for specific values of $t$, feel free to provide them! Would you like further details or have any specific questions?

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Additional Questions to Explore:

1. What will be the account balance after 5 years?
2. How long will it take for the account to double in value?
3. What is the annual growth rate of the account over time?
4. How does changing the interest rate to 12% affect the balance after 10 years?
5. What is the effect of compounding monthly instead of annually?

Tip:

For problems involving compound interest, always carefully identify the compounding frequency ($n$) and the time period (\