Determine the present value $P$ you must invest to have the future value $A$ at simple interest rate $r$ after time $t$.
\[
A=\$ 16,000, r=6.5 \%, t=4 \text { years }
\]
The present value that must be invested is $\$ \square$. (Round up to the nearest cent as needed.)
Answer
\(\boxed{P = \$12,698.41}\)
Step 1 ：Convert the interest rate from a percentage to a decimal by dividing by 100: \(r = 6.5\% = 0.065\)
Step 2 ：Rearrange the formula for future value to solve for present value: \(P = \frac{A}{1 + rt}\)
Step 3 ：Substitute the given values into the formula: \(P = \frac{\$16,000}{1 + 0.065 \times 4}\)
Step 4 ：Simplify the equation: \(P = \frac{\$16,000}{1 + 0.26}\)
Step 5 ：Calculate the present value: \(P = \frac{\$16,000}{1.26}\)
Step 6 ：\(\boxed{P = \$12,698.41}\)
