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 solve this, we can use the **future value formula** for compound interest:

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

Where:
- $FV$ = Future Value (the amount the account will be worth)
- $PV$ = Present Value (the amount you are depositing today, which is $3,200)
- $r$ = annual interest rate (9%, or 0.09)
- $t$ = number of years

### Future Value in 25 Years:
\[
FV_{25} = 3200 \times (1 + 0.09)^{25}
\]

### Future Value in 35 Years:
\[
FV_{35} = 3200 \times (1 + 0.09)^{35}
\]

Let's calculate both values.- In 25 years, your account will be worth **$27,593.86**.
- In 35 years, your account will be worth **$65,324.70**.

Would you like a detailed explanation of the compound interest process or have any other questions?

Here are some related questions to expand on this:
1. How would the future value change with a different interest rate?
2. What if you made regular annual deposits in addition to the initial deposit?
3. How does compounding frequency (monthly, quarterly) affect the future value?
4. What if the interest rate changed halfway through the investment period?
5. How can inflation affect the real value of your future savings?

**Tip:** The earlier you start investing, the more time compound interest has to grow your investment!

If you deposit ​$3,200 today into an account earning an annual rate of return of 9%, what will your account be worth in 25 years? In 35 years?

Discover how to calculate the future value of a $3,200 deposit with an annual return rate of 9%. This example demonstrates compound interest over 25 and 35 years, using the future value formula. Ideal for students learning financial mathematics and exponential growth.

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