Determine the present value P that must be invested to have the future value A at simple interest rate r after time t. 

a=$9000.00, r=12.0% t=6 months. do not round until the final answer. then round up to the nearest cent as needed.

To find the present value $ P $ needed to achieve a future value $ A $ using simple interest, we can use the formula:

\[
A = P(1 + rt)
\]

where:
- $ A $ is the future value,
- $ P $ is the present value (which we want to find),
- $ r $ is the interest rate per time period,
- $ t $ is the time in years.

Since we are given:
- $ A = 9000 $,
- $ r = 12\% = 0.12 $,
- $ t = 6 $ months $ = \frac{6}{12} = 0.5 $ years,

we can rearrange the formula to solve for $ P $:

\[
P = \frac{A}{1 + rt}
\]

Now, substitute the values:

\[
P = \frac{9000}{1 + (0.12 \times 0.5)}
\]

Calculating the denominator:

\[
1 + (0.12 \times 0.5) = 1 + 0.06 = 1.06
\]

Then,

\[
P = \frac{9000}{1.06} \approx 8490.57
\]

So, the present value $ P $ that must be invested is approximately **$8490.57**.

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Would you like more details on the steps? 

Here are 5 related questions:
1. How would the present value change if the interest rate increased?
2. What if the investment period changed from 6 months to 1 year?
3. How would compound interest affect the calculation for present value?
4. What if you needed to calculate the future value instead of the present value?
5. How does simple interest differ from compound interest?

**Tip:** Remember that with simple interest, the interest is not compounded, meaning it is calculated only on the initial principal.

Determine the present value P that must be invested to have the future value A at simple interest rate r after time t. A=$9000.00, r=12.0%, t=6 months. Do not round until the final answer. Then round up to the nearest cent as needed.

Learn how to calculate the present value needed to reach a future value of $9000 with a simple interest rate of 12% over 6 months. This problem demonstrates the use of simple interest formulas for students in Grades 9-12.

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