Gabriel deposits dollar sign, 660$660 every month into an account earning a monthly interest rate of 0.475%. How much would he have in the account after 16 months, to the nearest dollar? Use the following formula to determine your answer.

To find out how much Gabriel will have in his account after 16 months, we'll use the future value formula for 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 ($660).
- $ r $ is the monthly interest rate (0.475% or 0.00475 as a decimal).
- $ n $ is the number of months (16 months).

Let's calculate the amount:

\[
A = 660 \times \frac{(1 + 0.00475)^{16} - 1}{0.00475}
\]

First, calculate $ (1 + 0.00475)^{16} $:

\[
(1.00475)^{16} \approx 1.0777
\]

Then, subtract 1 from the result:

\[
1.0777 - 1 = 0.0777
\]

Now, divide this by $ r = 0.00475 $:

\[
\frac{0.0777}{0.00475} \approx 16.36
\]

Finally, multiply this by the monthly deposit $ P = 660 $:

\[
A = 660 \times 16.36 \approx 10,797.60
\]

Rounding to the nearest dollar, Gabriel would have approximately **$10,798** in the account after 16 months.

Would you like more details or have any questions?

Here are some related questions:
1. What would the total amount be if the interest rate increased to 0.5% per month?
2. How much more would Gabriel have after 24 months instead of 16 months?
3. What is the total interest earned during the 16 months?
4. How much would Gabriel need to deposit monthly to reach $15,000 after 16 months?
5. What if Gabriel made an initial lump sum deposit before starting the monthly deposits?

**Tip:** When dealing with compound interest, small changes in the interest rate or time period can significantly affect the final amount.

Learn how to calculate the future value of monthly deposits with compound interest using the formula. Example problem: Gabriel deposits $660 every month into an account earning 0.475% monthly interest. After 16 months, he will have approximately $10,798. Explore related questions like total interest earned and required monthly deposits.

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