You deposit $100 each month into an account earning 8% interest compounded monthly.
How much will you have in the account in 35 years?

To calculate how much you will have in the account in 35 years, we can use the **future value of a series** formula for compound interest. The formula is:

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

Where:
- $A$ = future value of the investment/loan, including interest
- $P$ = the monthly deposit amount = $100
- $r$ = annual interest rate (as a decimal) = 0.08
- $n$ = number of times interest is compounded per year = 12 (since it’s compounded monthly)
- $t$ = the number of years = 35

Let's calculate this step-by-step.The total amount you will have in the account after 35 years, with $100 monthly deposits and 8% interest compounded monthly, is approximately **$96,343.06**.

Would you like any further details or have any questions?

Here are 5 related questions for further exploration:
1. How does the total amount change if the interest rate is 6% instead of 8%?
2. What happens if you increase the monthly deposit to $200?
3. How much of the total amount is from your deposits versus the earned interest?
4. How would the future value differ if the interest was compounded annually rather than monthly?
5. How long would it take to double the investment if you deposit $100 per month at the same rate?

**Tip:** The longer you keep your money invested with compound interest, the more your interest earns additional interest, a phenomenon known as "interest on interest." This is why small monthly contributions can grow significantly over time!

You deposit $100 each month into an account earning 8% interest compounded monthly. How much will you have in the account in 35 years?

Learn how to calculate the future value of an account with $100 monthly deposits, 8% interest compounded monthly, over 35 years. This problem explores compound interest and the future value of a series formula. The total amount saved is approximately $96,343.06. Suitable for students in Grades 10-12.

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