If you deposit ​$3 comma 200 today into an account earning an annual rate of return of 9 ​percent, what will your account be worth in 25 years​ (assuming no further​ deposits)? In 35 ​years?

To calculate the future value of an investment, you can use the **compound interest formula**:

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

Where:
- $ A $ is the amount of money in the account after $ t $ years (future value),
- $ P $ is the initial principal (the amount you deposit),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years the money is invested.

Since the problem does not specify the compounding frequency, we will assume it is compounded annually, so $ n = 1 $.

For the given problem:
- $ P = 3200 $,
- $ r = 9\% = 0.09 $,
- $ n = 1 $,
- $ t = 25 $ years (for the first calculation) and $ t = 35 $ years (for the second calculation).

Let's calculate the future value for both 25 and 35 years.

### Future Value in 25 years:

\[
A = 3200 \left(1 + \frac{0.09}{1}\right)^{1 \times 25}
\]

### Future Value in 35 years:

\[
A = 3200 \left(1 + \frac{0.09}{1}\right)^{1 \times 35}
\]

I'll calculate these values now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the future values manually by plugging the numbers into the compound interest formula:

For 25 years:
\[
A = 3200 \times \left(1 + \frac{0.09}{1}\right)^{25}
\]

For 35 years:
\[
A = 3200 \times \left(1 + \frac{0.09}{1}\right)^{35}
\]

This will give you the account value after 25 and 35 years.

If you want any further clarification, feel free to ask!

Here are 5 related questions:
1. How does compounding frequency affect investment growth?
2. What is the difference between simple and compound interest?
3. How does the rate of return influence the future value of investments?
4. What are some strategies for achieving higher returns on investments?
5. How does inflation impact the real future value of investments?

**Tip:** The more frequently your interest is compounded, the more your investment will grow.

If you deposit ​$3,200 today into an account earning an annual rate of return of 9 ​percent, what will your account be worth in 25 years​ (assuming no further​ deposits)? In 35 ​years?

Learn how to calculate the future value of a $3,200 investment with an annual return of 9% over 25 and 35 years using the compound interest formula. This tutorial explores key concepts such as compound interest and exponential growth, suitable for students in Grades 9-12.

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