If you deposit ​$4 comma 000 today into an account earning an annual rate of return of 10 ​percent, what will your account be worth in 30 years​ (assuming no further​ deposits)? In 40 ​years?  


To find the future value of an investment with a fixed annual rate of return, we can use the formula for compound interest:

\[
\text{Future Value} = P \times \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ P $ is the principal amount (the initial 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 for.

In your case:
- $ P = 4000 $ dollars,
- $ r = 0.10 $ (10% annual return),
- $ n = 1 $ (since the interest is compounded annually),
- $ t = 30 $ years (for the first part of the question),
- $ t = 40 $ years (for the second part of the question).

### For 30 Years:

\[
\text{Future Value} = 4000 \times \left(1 + \frac{0.10}{1}\right)^{1 \times 30} = 4000 \times (1.10)^{30}
\]

### For 40 Years:

\[
\text{Future Value} = 4000 \times \left(1 + \frac{0.10}{1}\right)^{1 \times 40} = 4000 \times (1.10)^{40}
\]

Now, let's calculate the future values for both time periods.### Future Values:
- **In 30 years:** Your account will be worth **$69,797.61**.
- **In 40 years:** Your account will be worth **$181,037.02**.

Would you like any further details or have any questions?

Here are some related questions you might find interesting:
1. How does changing the interest rate affect the future value?
2. What if you made additional deposits each year?
3. How would the future value change if the interest were compounded monthly instead of annually?
4. What if the interest rate were variable instead of fixed?
5. How do taxes on interest affect the growth of the investment?

**Tip:** Compounding interest is powerful, especially over long periods, so even small changes in the rate or time can significantly impact the future value of an investment.

If you deposit ​$4,000 today into an account earning an annual rate of return of 10 percent, what will your account be worth in 30 years? In 40 years?

Find out how much $4,000 grows in 30 and 40 years with a 10% annual return using compound interest. Learn how to apply the future value formula to calculate the results step by step. Ideal for high school students studying exponential growth and financial math.

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