How much should you deposit at the end of each month into an investment account that pays 6.5% compounded monthly to have $4 million when you retire in 40 years?How much of the $4 million comes from earnings? In order to have $4 million in 40 years, you should deposit $? each month. Round up to the nearest dollar when needed.

To solve this problem, we'll use the **future value of an ordinary annuity** formula, as you're making regular monthly deposits into the investment account:

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

Where:
- $FV$ = Future Value (the amount you want to have at the end, which is $4,000,000),
- $P$ = Monthly deposit amount (this is what we want to find),
- $r$ = Monthly interest rate,
- $n$ = Total number of payments.

### Given information:
- The annual interest rate is 6.5%, so the monthly interest rate $r = \frac{6.5\%}{12} = 0.005417$,
- You want to retire in 40 years, so the total number of monthly payments $n = 40 \times 12 = 480$.

Now, we can rearrange the formula to solve for $P$:

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

Let me calculate the monthly deposit and the total earnings.To accumulate $4 million in 40 years, you should deposit **$1,752** at the end of each month.

### Breakdown:
- Total contributions (your deposits): $840,771
- Total earnings (from interest): $3,159,229

Would you like more details or have any questions?

Here are 5 follow-up questions to consider:
1. How does changing the interest rate affect the monthly deposit?
2. What if you wanted to retire in 30 years instead of 40?
3. How would increasing the monthly deposit change the time to reach $4 million?
4. What if the interest was compounded annually instead of monthly?
5. How does inflation affect the future value of your retirement savings?

**Tip:** Starting early with regular contributions allows compound interest to grow your investments more effectively!

How much should you deposit at the end of each month into an investment account that pays 6.5% compounded monthly to have $4 million when you retire in 40 years? How much of the $4 million comes from earnings?

Find out how much you need to deposit monthly to retire with $4 million in 40 years. Learn about the future value of an annuity, compound interest, and see a breakdown of total contributions and earnings. Ideal for college-level financial mathematics students.

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