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

A​ =

​$6000,

r​ =

3.5,

t​ =

5

years

To determine the present value $ P $ that must be invested to achieve a future value $ A $ under simple interest, we use the simple interest formula:

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

Where:
- $ A $ is the future value,
- $ P $ is the present value (what we're solving for),
- $ r $ is the interest rate (in decimal form),
- $ t $ is the time in years.

### Given values:
- $ A = 6000 $
- $ r = 3.5\% = 0.035 $
- $ t = 5 $ years

We rearrange the formula to solve for $ P $:

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

Substitute the given values:

\[
P = \frac{6000}{1 + (0.035 \times 5)}
\]

Let's calculate this.The present value $ P $ that must be invested to achieve a future value of $6000 at a simple interest rate of 3.5% over 5 years is approximately **$5106.38**.

Would you like more details or have any questions?

Here are some related questions you might explore:
1. How would the present value change if the interest rate increased to 5%?
2. How much interest is earned over the 5-year period?
3. What would the present value be for a future value of $10,000 under the same conditions?
4. How does compound interest differ from simple interest in calculating present value?
5. What happens to the present value if the time period is extended to 10 years?

**Tip:** When working with simple interest, always convert percentages to decimals before using them in calculations!

Determine the present value P that must be invested to have the future value A at simple interest rate r after time t. A = $6000, r = 3.5%, t = 5 years.

Learn how to calculate the present value that must be invested to achieve a future value of $6000 at a simple interest rate of 3.5% over 5 years. This problem involves simple interest formulas and algebraic rearrangement, suitable for Grades 9-12 students.

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