Suppose you want to have $400,000 for retirement in 25 years. Your account earns 5% interest. How much would you need to deposit in the account each month?

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To determine how much you need to deposit monthly to have $400,000 in 25 years with an interest rate of 5%, we can use the formula for the future value of an annuity:

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

Where:
- $ FV $ is the future value (\$400,000),
- $ P $ is the monthly deposit (what we are solving for),
- $ r $ is the annual interest rate (5% or 0.05),
- $ n $ is the number of times the interest is compounded per year (since it's monthly deposits, $ n = 12 $),
- $ t $ is the time in years (25 years).

Rearranging the formula to solve for $ P $:

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

Now, let's calculate it step by step.

\[
P = \frac{400,000}{\frac{(1 + 0.05/12)^{12 \times 25} - 1}{0.05/12}}
\]

I'll compute that.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still apply the future value of an annuity formula I shared earlier to calculate it manually. If you have any questions, I’d be happy to explain further!

Would you like more details on this approach or another math topic? 

Here are some related questions:
1. How would the monthly deposit change if the interest rate increased to 6%?
2. What if the retirement goal was $500,000 instead of $400,000?
3. How does the time period affect the required monthly deposit?
4. What happens if the interest compounds quarterly instead of monthly?
5. How do changes in inflation affect retirement savings goals?

**Tip:** When solving finance problems, it's useful to keep track of how often the interest is compounded, as it affects the total amount accumulated over time.

Suppose you want to have $400,000 for retirement in 25 years. Your account earns 5% interest. How much would you need to deposit in the account each month?

Calculate how much you need to deposit monthly to reach a $400,000 retirement goal in 25 years, with a 5% interest rate. This problem uses the future value of an annuity formula and explores concepts such as compound interest and annuities. Perfect for Grades 10-12.

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