How much should you deposit at the end of each month into an investment account that pays 8.5 % compounded monthly to have $2 million when you retire in 44 years? How much of the $2 million comes from​ earnings?

In order to have ​$2 million in 44 years, you should deposit ​$enter your response here each month.(Round up to the nearest​ dollar.)

$ enter your response here of the ​$2 million comes from interest. (Round up to the nearest​ dollar.)

To solve this problem, we need to use the **future value of an ordinary annuity** formula, because deposits are made at the *end* of each month:

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

Where:
- $ FV $ is the future value, which is $2,000,000.
- $ P $ is the monthly deposit.
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of deposits (number of years times 12).

### Breakdown:
1. **Future Value**: $ FV = 2,000,000 $.
2. **Annual Interest Rate**: $ 8.5\% $, or $ 0.085 $.
3. **Monthly Interest Rate**: $ r = \frac{0.085}{12} \approx 0.0070833 $.
4. **Number of Deposits**: $ n = 44 \times 12 = 528 $.

Now, solving for $ P $:

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

I'll calculate the monthly deposit ($ P $) and then determine how much of the $2,000,000 comes from the contributions and interest.To reach $2 million in 44 years, you should deposit **$349** at the end of each month.

Out of the $2 million, **$1,815,521** comes from interest earnings, while the rest comes from your monthly contributions.

Let me know if you'd like more details or have any questions!

### Related Questions:
1. How would the monthly deposit change if the interest rate was 6% instead?
2. What would happen to the monthly deposit if the retirement period was reduced to 30 years?
3. How much would you have after 44 years if you deposited $500 monthly instead?
4. What is the total amount deposited over the 44 years?
5. What if the compounding period was quarterly instead of monthly?

### Tip:
For long-term investments, even small differences in interest rates can have a significant impact on the final amount. Consider the power of compounding when choosing your investment strategy.

How much should you deposit at the end of each month into an investment account that pays 8.5% compounded monthly to have $2 million when you retire in 44 years? How much of the $2 million comes from​ earnings?

Learn how to calculate the monthly deposit needed to reach $2 million in 44 years with an interest rate of 8.5%, compounded monthly. This problem covers key financial math concepts, including the future value of an ordinary annuity and compound interest. The solution provides detailed steps, including the amount earned from interest.

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