Mila deposits dollar sign, 360$360 every month into an account earning a monthly interest rate of 0.75%. How much would she have in the account after 5 months, to the nearest dollar? Use the following formula to determine your answer.

To calculate the total amount in Mila's account after 5 months, we can use the following formula for the future value of a series of equal monthly deposits with compound interest:

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

Where:
- $ A $ is the amount in the account after $ n $ months.
- $ P $ is the monthly deposit (in this case, $360).
- $ r $ is the monthly interest rate (0.75% or 0.0075 as a decimal).
- $ n $ is the number of months (5 months in this case).

Let's calculate the amount:

\[
A = 360 \times \frac{(1 + 0.0075)^5 - 1}{0.0075}
\]

First, we calculate $ (1 + 0.0075)^5 $:

\[
(1.0075)^5 \approx 1.0381
\]

Then, subtract 1 from the result:

\[
1.0381 - 1 = 0.0381
\]

Now, divide this by $ r = 0.0075 $:

\[
\frac{0.0381}{0.0075} \approx 5.08
\]

Finally, multiply this by the monthly deposit $ P = 360 $:

\[
A = 360 \times 5.08 \approx 1830
\]

So, after 5 months, Mila would have approximately **$1,830** in the account.

Would you like more details or have any questions?

Here are some related questions:
1. What is the future value if the interest rate were 1% per month?
2. How does the final amount change if she deposits $400 instead of $360?
3. What would be the total interest earned after 5 months?
4. How much would Mila have after 12 months under the same conditions?
5. What if the deposits were made quarterly instead of monthly?

**Tip:** Always ensure your interest rate and time period units match when using financial formulas.

Learn how to calculate the future value of monthly deposits with compound interest using Mila's example. This problem involves understanding compound interest and the future value of annuities formula. Suitable for high school students and anyone interested in financial mathematics.

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