You put ​$400 per month in an investment plan that pays an APR of 3.5​%. How much money will you have after 20 ​years? Compare this amount to the total deposits made over the time period.

To solve this problem, we can use the formula for the future value of a series of monthly investments in an account that earns compound interest. The formula is:

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

Where:
- $A$ is the future value of the investment.
- $P$ is the monthly deposit.
- $r$ is the annual interest rate (as a decimal).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the number of years.

### Given:
- Monthly deposit $P = 400$
- Annual interest rate $r = 3.5\% = 0.035$
- Compounded monthly, so $n = 12$
- Time period $t = 20$ years

Let's plug these values into the formula and compute the future value of your investment. Then we will compare this value to the total deposits made.

I'll calculate it now.After 20 years of investing \$400 per month at an APR of 3.5%, the total amount in the account will be approximately **\$138,747.71**.

The total deposits made over 20 years will be:
\[
400 \, \text{(monthly deposit)} \times 12 \, \text{(months per year)} \times 20 \, \text{(years)} = 96,000
\]

### Comparison:
- **Total deposits**: \$96,000
- **Future value of investment**: \$138,747.71
- **Interest earned**: \$138,747.71 - \$96,000 = \$42,747.71

This shows that you've earned \$42,747.71 in interest over the 20 years.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the future value change with a higher interest rate?
2. What happens if the investment period is extended to 30 years?
3. How does the frequency of compounding affect the future value?
4. What if you increase the monthly deposit by \$100 every 5 years?
5. How much interest would you earn if there were no compounding?

**Tip:** Even small differences in interest rates can lead to substantial changes in the future value due to the power of compounding.

You put $400 per month in an investment plan that pays an APR of 3.5%. How much money will you have after 20 years? Compare this amount to the total deposits made over the time period.

Calculate the future value of a $400 monthly investment over 20 years at 3.5% APR using the compound interest formula. This investment grows to $138,747.71, compared to $96,000 in total deposits, earning $42,747.71 in interest. Explore how compound interest affects investment growth.

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