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

$A = P(1 + rt)$

where:

• $A$ is the future value (in this case, $8000),
• $r$ is the simple interest rate as a decimal,
• $t$ is the time in years,
• $P$ is the present value we need to find.

Step 1: Convert Variables

Given:

• $A = 8000$,
• $r = 14.0\% = 0.14$ (as a decimal),
• $t = 99$ months.

Since $t$ needs to be in years, convert months to years: $t = \frac{99}{12} = 8.25 \text{ years}$

Step 2: Substitute Values and Rearrange for $P$

Rearrange the formula to solve for $P$: $P = \frac{A}{1 + rt}$

Substitute the values: $P = \frac{8000}{1 + (0.14 \times 8.25)}$

Step 3: Calculate

Calculate the term in the denominator: $1 + (0.14 \times 8.25) = 1 + 1.155 = 2.155$

Then: $P = \frac{8000}{2.155} \approx 3711.13$