You deposit $5000 in an account earning 4% interest compounded monthly. How much will you have in the account in 15 years?

To determine the future value of the account, we can use the formula for compound interest:

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

Where:
- $A$ = the amount of money in the account after interest.
- $P$ = the principal amount (initial deposit) = $5000.
- $r$ = the annual interest rate = 4% or 0.04.
- $n$ = the number of times interest is compounded per year = 12 (monthly compounding).
- $t$ = the number of years the money is invested = 15.

Now, plugging the values into the formula:

\[
A = 5000 \left(1 + \frac{0.04}{12}\right)^{12 \times 15}
\]

Let's calculate that.After 15 years, the account will grow to approximately **$9101.51** with the 4% interest compounded monthly.

Would you like any more details or have any further questions?

Here are some related questions you might find interesting:
1. What if the interest rate was 5% instead of 4%?
2. How would the amount change if the interest was compounded quarterly instead of monthly?
3. What is the total interest earned over the 15 years?
4. How long would it take to double the initial deposit at the same interest rate?
5. What happens if you make additional monthly deposits into the account?

**Tip**: Increasing the frequency of compounding (e.g., monthly vs annually) slightly increases the final amount due to the effect of more frequent interest accumulation.

Find out how to calculate the future value of $5000 with 4% interest compounded monthly over 15 years. Using the compound interest formula, learn how much the account grows to and understand the principles of exponential growth in finance. Suitable for Grades 10-12.

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