You deposit $3000 each year into an account earning 4% interest compounded annually. How much will you have in the account in 15 years?

To solve this problem, we can use the **future value of an annuity formula** because you are making regular annual deposits and the interest is compounded annually.

The formula is:

\[
A = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $A$ is the future value of the annuity (the amount in the account after 15 years),
- $P$ is the annual deposit (\$3000),
- $r$ is the interest rate per period (4% or 0.04),
- $n$ is the number of periods (15 years).

Let's plug in the values:

\[
A = 3000 \times \frac{(1 + 0.04)^{15} - 1}{0.04}
\]

Now, let's calculate this.

After 15 years, the account will have approximately **$60,070.76**.

Would you like more details or have any questions about this calculation?

Here are five related questions for deeper understanding:
1. What if you deposited $4000 each year instead of $3000?
2. How would the future value change if the interest rate were 5% instead of 4%?
3. What would happen if you compounded the interest semi-annually instead of annually?
4. How much interest will you earn in total over the 15 years?
5. How would a different deposit schedule, such as monthly deposits, affect the outcome?

**Tip:** Always remember that compounding frequency can greatly impact the future value of your investment.

Calculate the future value of depositing $3000 each year into an account with 4% interest compounded annually over 15 years. This problem uses the future value of an annuity formula and covers key financial math concepts like compound interest and exponential growth. Suitable for high school students in Grades 10-12.

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