How much would you need to deposit in an account now in order to have $5000 in the account in 5 years? Assume the account earns 8% interest compounded quarterly. Round your answer to the nearest cent.

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To determine how much you need to deposit now in order to have $5000 in the account in 5 years, with an interest rate of 8% compounded quarterly, we use the **present value formula** for compound interest:

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

Where:
- $ PV $ = present value (the amount you need to deposit now),
- $ FV $ = future value (the amount you want in the future, which is $5000),
- $ r $ = annual interest rate (8% or 0.08),
- $ n $ = number of times the interest is compounded per year (quarterly, so $ n = 4 $),
- $ t $ = number of years (5 years).

### Substituting the given values:
\[
PV = \frac{5000}{(1 + \frac{0.08}{4})^{4 \times 5}}
\]

Let's calculate this.The amount you need to deposit now in order to have $5000 in 5 years, with an 8% interest rate compounded quarterly, is approximately **$3364.86**.

Would you like more details, or have any further questions? 

Here are five related questions:
1. How does changing the compounding frequency affect the amount you need to deposit?
2. What would the required deposit be if the interest rate were 6% instead of 8%?
3. How does the time period (years) impact the initial deposit needed?
4. What would be the future value if you deposited $5000 now with the same interest rate?
5. How does simple interest differ from compound interest in scenarios like this?

**Tip:** The more frequently interest is compounded, the less you need to deposit initially to reach the same future value.

How much would you need to deposit in an account now in order to have $5000 in the account in 5 years? Assume the account earns 8% interest compounded quarterly. Round your answer to the nearest cent.

Learn how to calculate how much you need to deposit now to reach $5000 in 5 years with an 8% interest rate compounded quarterly. This solution uses the present value formula for compound interest, making it suitable for students in Grades 10-12.

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