7 Formula 1 point Suppose you expect to receive a cash flow of \( \$ 14,000 \) exactly 8 years from today. If the discount rate is \( 7 \% \), what is today's cash equivalent to this future amount? Round your answer to thenearest penry. Type your answer.

To find the present value of a future amount, we can use the formula for present value: \[ PV = \frac{FV}{(1 + r)^n} \] where: - \( PV \) is the present value, - \( FV \) is the future value, - \( r \) is the discount rate, - \( n \) is the number of years. Given: - \( FV = \$14,000 \), - \( r = 7\% = 0.07 \), - \( n = 8 \) years. Substitute the values into the formula: \[ PV = \frac{14,000}{(1 + 0.07)^8} \] Now, we can calculate the present value using the formula. Calculate the value by following steps: - step0: Calculate: \(\frac{14000}{\left(1+0.07\right)^{8}}\) - step1: Add the numbers: \(\frac{14000}{1.07^{8}}\) - step2: Convert the expressions: \(\frac{14000}{\left(\frac{107}{100}\right)^{8}}\) - step3: Simplify the expression: \(\frac{14000}{\frac{107^{8}}{100^{8}}}\) - step4: Rewrite the expression: \(\frac{14000\times 100^{8}}{107^{8}}\) The present value of the future amount of $14,000, discounted at a rate of 7% over 8 years, is approximately $8,148.13. Rounding to the nearest penny, the present value is $8,148.13.