k Determine the present value P that must be invested to have the future value A at simple interest rate $r$ after time $t$. \[ A=\$ 6500, r=4.5 \%, t=3 \text { years } \] The present value $\mathrm{P}$ that must be invested is $\$ \square$. (Round up to the nearest cent as nesded.)

Step 1 ：We are given the future value of the investment A = $6500, the annual interest rate r = 4.5%, and the time the money is invested for t = 3 years. We need to determine the present value P that must be invested.

Step 2 ：The formula for the future value of an investment using simple interest is given by: \( A = P(1 + rt) \)

Step 3 ：We can rearrange the formula to solve for P: \( P = \frac{A}{1 + rt} \)

Step 4 ：Substitute the given values into the formula: A = 6500, r = 0.045 (4.5% as a decimal), and t = 3.

Step 5 ：Calculate P: \( P = \frac{6500}{1 + 0.045 \times 3} \)

Step 6 ：Final Answer: The present value P that must be invested is \(\boxed{5726.87}\)