Determine the present value P that must be invested to have the future value A at simple interest rate r after time t. 
A​ = ​$4000.00​, r​ = 12.5​%, t​ = 6 months
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Part 1
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enter your response here ​(Do not round until the final answer. Then round up to the nearest cent as​ needed.)

To calculate the present value $ P $ that must be invested to reach the future value $ A $ using simple interest, we use the formula:

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

Where:
- $ A $ is the future value
- $ P $ is the present value
- $ r $ is the interest rate (as a decimal)
- $ t $ is the time in years

Given:
- $ A = 4000 $ (future value)
- $ r = 12.5\% = 0.125 $ (interest rate as a decimal)
- $ t = 6 $ months $ = \frac{6}{12} = 0.5 $ years

We rearrange the formula to solve for $ P $:

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

Now, substituting the given values:

\[
P = \frac{4000}{1 + (0.125 \times 0.5)}
\]

Let's calculate that.The present value $ P $ that must be invested is approximately $ 3764.71 $.

Would you like further details or have any questions?

Here are some related questions:
1. How does simple interest differ from compound interest in this scenario?
2. How would the present value change if the time period was 1 year instead of 6 months?
3. How would the calculation change if the interest was compounded monthly?
4. What is the formula for finding the future value in simple interest?
5. What happens if the interest rate is doubled but the time remains the same?

**Tip:** Always convert time to years when dealing with interest rate calculations, as rates are often given on a per-year basis.

Determine the present value P that must be invested to have the future value A at simple interest rate r after time t. A = $4000.00, r = 12.5%, t = 6 months

Learn how to calculate the present value required to achieve a future value of $4000 at a 12.5% simple interest rate over 6 months. This problem covers key algebraic concepts and simple interest calculations. Suitable for students in Grades 9-11.

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