How much would you need to deposit in an account now in order to have $3000 in the account in 15 years? Assume the account earns 8% interest compounded quarterly. Round your answer to the nearest cent.

To determine how much to deposit now to have $3,000 in 15 years with 8% interest compounded quarterly, we can use the formula for compound interest:

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

Where:
- $ A $ is the future value ($3,000),
- $ P $ is the present value (the amount to be deposited),
- $ r $ is the annual interest rate (8% or 0.08),
- $ n $ is the number of times the interest is compounded per year (quarterly compounding means $ n = 4 $),
- $ t $ is the number of years (15 years).

We need to solve for $ P $. Rearranging the formula to solve for $ P $:

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

Substitute the given values into the formula:

\[
P = \frac{3000}{\left(1 + \frac{0.08}{4}\right)^{4 \times 15}}
\]

Let's calculate this step-by-step.The amount you would need to deposit now in order to have $3,000 in the account in 15 years, with an 8% interest rate compounded quarterly, is approximately **$914.35**.

Would you like further details on the calculation or have any additional questions?

Here are some related questions you might find useful:
1. What happens to the deposit amount if the interest rate is 5% instead of 8%?
2. How would the deposit amount change if the interest is compounded monthly?
3. What would be the future value if you deposited $914.35 at an annual rate of 6% compounded quarterly for 20 years?
4. How do interest rates affect the time required to double an investment?
5. Can you explain the difference between simple interest and compound interest?

**Tip:** The more frequently interest is compounded, the faster the amount grows due to the effect of earning interest on interest.

Learn how to calculate the initial deposit needed to grow to $3,000 in 15 years with an 8% interest rate compounded quarterly. This step-by-step guide covers compound interest and financial mathematics, suitable for students in Grades 10-12.

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