You deposit $500 each month into an account earning 5% interest compounded monthly.
How much total interest will you earn over 20 years?

To calculate the total interest earned over 20 years with monthly deposits, we can use the formula for the future value of an annuity with compound interest:

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

Where:
- $ P $ is the monthly deposit ($500).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of deposits (number of years times 12).
- $ FV $ is the future value of the annuity.

Given:
- $ P = 500 $ dollars
- Annual interest rate = 5%, so $ r = \frac{5\%}{12} = \frac{0.05}{12} \approx 0.004167 $
- $ n = 20 \times 12 = 240 $ months

First, we calculate the future value $ FV $:

\[
FV = 500 \times \frac{(1 + 0.004167)^{240} - 1}{0.004167}
\]

Let's calculate that.The future value of the annuity after 20 years will be approximately $205,516.83.

To find the total interest earned, subtract the total amount of deposits from the future value:

- Total amount deposited: $ 500 \times 240 = 120,000 $ dollars.
- Total interest earned: $ 205,516.83 - 120,000 = 85,516.83 $ dollars.

So, the total interest earned over 20 years is approximately **$85,516.83**.

Would you like more details or have any questions? Here are some related questions:

1. How would the total interest change if the interest rate were 6% instead of 5%?
2. What happens to the future value if you deposit $600 instead of $500 each month?
3. How does changing the deposit frequency (e.g., quarterly instead of monthly) affect the interest earned?
4. What is the total interest earned if the account compounds interest quarterly instead of monthly?
5. How much would you need to deposit monthly to reach a future value of $300,000 after 20 years?

**Tip:** The frequency of compounding can significantly affect the total interest earned over time. Monthly compounding usually results in higher interest compared to annual or quarterly compounding.

Learn how to calculate the total interest earned over 20 years with monthly deposits of $500 into an account earning 5% interest compounded monthly. Understand the future value of an annuity formula and how it applies to compound interest calculations. Total interest earned: $85,516.83.

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