You deposit $4000 in an account earning 5% interest compounded monthly. How much will you have in the account in 15 years?

To calculate how much you'll have in the account after 15 years with monthly compounded interest, we use the formula for compound interest:

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

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

### Given:
- $P = 4000$,
- $r = 0.05$ (5% annual interest),
- $n = 12$ (compounded monthly),
- $t = 15$.

Now plug the values into the formula:

\[
A = 4000 \left(1 + \frac{0.05}{12}\right)^{12 \times 15}
\]

\[
A = 4000 \left(1 + 0.004167\right)^{180}
\]

\[
A = 4000 \left(1.004167\right)^{180}
\]

\[
A \approx 4000 \times 2.114
\]

\[
A \approx 8456.06
\]

So, after 15 years, the amount in the account will be approximately **$8,456.06**.

Would you like more details or have any further questions?

Here are some related questions to consider:
1. What would the total interest earned be over the 15 years?
2. How would the final amount change if the interest was compounded quarterly instead of monthly?
3. What if the interest rate was 6% instead of 5%?
4. How would the final amount be affected if the deposit was increased to $5000?
5. How much would the account hold after 10 years instead of 15?

**Tip**: The more frequently interest is compounded, the higher the final amount, due to the interest-on-interest effect.

Discover how to calculate compound interest on a $4000 deposit with 5% interest compounded monthly over 15 years. This solution uses the compound interest formula A = P(1 + r/n)^(nt) and is ideal for students in Grades 9-12.

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