suppose you want to have $600000 for retirement in 25 years. Your account earns 8% interest. Round your answers to the nearest cent.
A) how much would you need to deposit in the account each month?

To find how much you would need to deposit each month, we can use the formula for the future value of an annuity, which accounts for regular monthly deposits into an account that earns compound interest:

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

Where:
- $FV$ is the future value (in this case, $600,000),
- $P$ is the monthly deposit,
- $r$ is the annual interest rate (8% or 0.08),
- $n$ is the number of times the interest is compounded per year (since it's monthly, $n = 12$),
- $t$ is the number of years (25 years).

We need to solve for $P$, the monthly deposit:

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

Now let's calculate the monthly deposit amount. I'll do the math step by step.You would need to deposit approximately **$630.90** each month to have $600,000 for retirement in 25 years, assuming an 8% annual interest rate.

Do you want more details on how this was calculated or have any other questions?

Here are five related questions:
1. How does the interest rate affect the monthly deposit amount?
2. What if the interest is compounded quarterly instead of monthly?
3. How would the required deposit change if you wanted to retire in 20 years instead of 25?
4. What happens if you increase the monthly deposit amount to $700? How much would you have in 25 years?
5. What if you start with an initial deposit of $10,000?

**Tip:** The earlier you start saving, the less you'll need to deposit each month due to the power of compound interest.

Suppose you want to have $600,000 for retirement in 25 years. Your account earns 8% interest. How much would you need to deposit in the account each month?

Find out how to calculate the monthly deposits needed to reach $600,000 for retirement in 25 years, earning 8% interest. Learn key concepts like compound interest, annuities, and the future value formula. Suitable for high school students and those planning their finances.

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