How much would you need to deposit in an account now in order to have
$6,000 in the account in 8 years? Assume the account earns 6% interest compounded
monthly. (Round the answer to two decimal place accuracy.

To calculate how much you would need to deposit now (the present value $ P $) in order to have $6,000 in 8 years with a 6% interest rate compounded monthly, we can use the **Present Value formula for compound interest**:

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

Where:
- $ P $ = present value (the amount you need to deposit now)
- $ A $ = future value (the amount you want in the future, $6,000)
- $ r $ = annual interest rate (6%, or 0.06)
- $ n $ = number of times the interest is compounded per year (monthly compounding, so $ n = 12 $)
- $ t $ = number of years (8 years)

Now, let's substitute the values and calculate $ P $. 

\[
P = \frac{6000}{(1 + \frac{0.06}{12})^{12 \times 8}}
\]

I'll compute the value for you.The amount you would need to deposit now in order to have $6,000 in 8 years with a 6% interest rate compounded monthly is approximately **$3,717.14**.

Would you like more details on the calculation? Here are some related questions you might find useful:

1. How does changing the interest rate affect the required deposit?
2. What if the interest was compounded quarterly instead of monthly?
3. How much would you need to deposit if the target amount was $10,000 instead?
4. What if the deposit term was 10 years instead of 8?
5. How does simple interest differ from compound interest in such scenarios?

**Tip:** Compounding more frequently (monthly, daily) will reduce the amount you need to deposit now compared to annual compounding.

How much would you need to deposit in an account now in order to have $6,000 in the account in 8 years? Assume the account earns 6% interest compounded monthly. (Round the answer to two decimal places.)

Learn how to calculate the present value required to reach $6,000 in 8 years with 6% interest compounded monthly. This solution uses the compound interest formula to determine the initial deposit needed. Suitable for Grades 11-12 students exploring exponential growth and finance math concepts.

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