you deposit $4000 in an account earning 3% interest compounded monthly. How much will you have in the account in 15 years?

To find out how much you will have in the account after 15 years with monthly compounding interest, you can use the formula for compound interest:

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

Where:
- $A$ is the amount of money accumulated after n years, including interest.
- $P$ is the principal amount (the initial deposit or investment).
- $r$ is the annual interest rate (decimal).
- $n$ is the number of times that interest is compounded per year.
- $t$ is the number of years the money is invested or borrowed.

For this problem:
- $P = 4000$
- $r = 0.03$
- $n = 12$ (since interest is compounded monthly)
- $t = 15$

Substituting these values into the formula:

\[
A = 4000 \left(1 + \frac{0.03}{12}\right)^{12 \times 15}
\]

Calculating the expression inside the parentheses:

\[
A = 4000 \left(1 + 0.0025\right)^{180}
\]
\[
A = 4000 \left(1.0025\right)^{180}
\]

Now calculating $ (1.0025)^{180} $:

\[
(1.0025)^{180} \approx 1.491825
\]

Now, multiply by the principal:

\[
A \approx 4000 \times 1.491825 \approx 5967.30
\]

Thus, after 15 years, you will have approximately **$5,967.30** in the account.

### Do you want more details or have any questions?

Here are some related questions to consider:
1. How would the amount change if the interest rate were 4% instead of 3%?
2. What would the final amount be if interest was compounded annually?
3. How much total interest would you earn over the 15 years?
4. What happens to the final amount if you increase the deposit to $5000?
5. How would the account value change if compounded quarterly instead of monthly? 

**Tip:** Regularly reviewing your investment options can lead to better interest rates and greater earnings over time.

You deposit $4000 in an account earning 3% interest compounded monthly. How much will you have in the account in 15 years?

Discover how to calculate the future value of a $4000 investment at 3% interest compounded monthly over 15 years. This guide covers the compound interest formula and provides a step-by-step solution, ideal for students and individuals interested in finance.

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