If you deposit $100 every month into an account which pays 3.6% interest, compounded monthly, how much money will you have in your account after 9 years?

Round your answer to the nearest whole dollar.

To calculate the amount of money in your account after 9 years with monthly deposits and compound interest, we can use the future value of an annuity formula:

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

Where:
- $ A $ is the future value of the investment.
- $ P $ is the monthly deposit amount (\$100).
- $ r $ is the monthly interest rate.
- $ n $ is the total number of deposits.

First, let's break down the components:
- The annual interest rate is 3.6%, so the monthly interest rate $ r $ is:

\[
r = \frac{3.6\%}{12} = \frac{0.036}{12} = 0.003
\]

- The number of months $ n $ over 9 years is:

\[
n = 9 \times 12 = 108 \text{ months}
\]

Now, we can plug in the values:

\[
A = 100 \times \frac{{(1 + 0.003)^{108} - 1}}{0.003}
\]

Let's calculate this step by step.

\[
(1 + 0.003)^{108} = (1.003)^{108} \approx 1.34935355
\]

\[
A = 100 \times \frac{{1.34935355 - 1}}{0.003} \approx 100 \times \frac{0.34935355}{0.003} \approx 100 \times 116.4511833 \approx 11645.12
\]

After rounding to the nearest whole dollar:

\[
A \approx 11,645
\]

So, after 9 years, the amount of money in the account will be approximately **$11,645**.

Would you like more details or have any questions? Here are five related questions for further exploration:

1. How does increasing the monthly deposit affect the future value after 9 years?
2. What if the interest rate were compounded quarterly instead of monthly?
3. How would the total amount change if the interest rate were 4% instead of 3.6%?
4. What would be the impact of withdrawing a portion of the money yearly on the future value?
5. How does the time period (e.g., 15 years instead of 9 years) influence the future value?

**Tip:** To maximize your returns, always compare different compounding intervals when choosing an investment plan.

If you deposit $100 every month into an account which pays 3.6% interest, compounded monthly, how much money will you have in your account after 9 years? Round your answer to the nearest whole dollar.

Calculate the future value of monthly deposits of $100 at a 3.6% interest rate compounded monthly over 9 years. Learn the formula and steps to find the final amount, perfect for high school students in Grades 10-12.

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