Suppose you want to have $400,000 for retirement in 20 years. Your account earns 4% interest. How much would you need to deposit in the account each month?

To determine how much you need to deposit each month to reach $400,000 in 20 years, we can use the formula for the future value of a series of regular deposits, also known as an ordinary annuity:

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

Where:
- $ FV $ = future value ($400,000)
- $ P $ = monthly deposit amount (unknown, what we're solving for)
- $ r $ = monthly interest rate (annual rate divided by 12 months)
- $ n $ = total number of deposits (number of years multiplied by 12)

Given:
- Annual interest rate: 4% (0.04 as a decimal)
- Number of years: 20
- Monthly interest rate: $ \frac{0.04}{12} $
- Total number of deposits: $ 20 \times 12 = 240 $

Substituting the values:

\[
400,000 = P \times \frac{(1 + \frac{0.04}{12})^{240} - 1}{\frac{0.04}{12}}
\]

Now, let's solve for $ P $.The amount you need to deposit each month is approximately **$1,090.59**.

Would you like to see more details on how this was calculated, or do you have any further questions?

Here are some related questions you might find useful:

1. How would the monthly deposit change if the interest rate was 5% instead of 4%?
2. What would be the future value if you deposited $1,000 each month instead?
3. How much would you need if you want to retire in 15 years instead of 20 years?
4. How does changing the compounding frequency affect the required deposit amount?
5. What happens if you make the deposit at the beginning of each month instead of the end?

**Tip:** Compounding frequency significantly impacts the total amount accumulated; more frequent compounding increases the future value.

Learn how to calculate the monthly deposit needed to save $400,000 in 20 years with a 4% annual interest rate. This guide explains key concepts like annuities, compound interest, and the future value formula, suitable for students in Grades 10-12 and anyone planning for retirement.

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