You wish to have $23,000 in 8 years. Use Table 11-2 to create a new table factor, and then find how much you should invest now (in $) at 6% interest, compounded quarterly in order to have $23,000, 8 years from now. (Round your answer to the nearest cent.)
$

To solve this problem, we will use the **present value formula** for compound interest. Since the interest is compounded quarterly, we’ll adjust the rate and number of periods accordingly.

The formula for **present value** $ P $ is:

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

Where:
- $ A $ is the future value (which is \$23,000),
- $ r $ is the annual interest rate (6% = 0.06),
- $ n $ is the number of times the interest is compounded per year (quarterly, so $ n = 4 $),
- $ t $ is the time in years (8 years),
- $ P $ is the present value, or the amount to invest now.

### Step-by-step breakdown:

1. **Given Values:**
   - Future value $ A = 23,000 $
   - Annual interest rate $ r = 6\% = 0.06 $
   - Compounding periods per year $ n = 4 $ (quarterly)
   - Time $ t = 8 $ years

2. **Calculate $ P $ (Present Value):**

\[
P = \frac{23,000}{(1 + \frac{0.06}{4})^{4 \times 8}}
\]

Now, let's compute this value.The amount you should invest now is approximately **$14,282.84** to have $23,000 in 8 years at 6% interest, compounded quarterly.

Would you like further details or have any questions? Here are 5 related questions to expand on this concept:

1. How does changing the compounding frequency affect the amount you need to invest?
2. What would the investment amount be if the interest rate was 5% instead of 6%?
3. How does the investment amount change if the goal is reached in 10 years instead of 8?
4. What is the formula for future value in compound interest?
5. How can you calculate the future value if compounding is done continuously?

**Tip:** When dealing with compound interest, the more frequently interest is compounded, the greater the future value due to the effect of interest-on-interest.

You wish to have $23,000 in 8 years. Use Table 11-2 to create a new table factor, and then find how much you should invest now (in $) at 6% interest, compounded quarterly in order to have $23,000, 8 years from now. (Round your answer to the nearest cent.)

Learn how to calculate how much you should invest today to have $23,000 in 8 years with 6% interest compounded quarterly. This problem applies the compound interest formula to solve for present value. Suitable for high school students, Grades 10-12.

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