0/6 Points] DETAILS MY NOTES. WANEFMAC8 3.2.045. PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANOT Inflation has been running \( 4 \% \) per year. A car now costs \( \$ 30,000 \). How much (in dollars) would it have cost 2 years ago? (Round your answer to the nearest cent.) \( \$ 27,732.00 \mathrm{x} \) Need Help? Readil Whtch

To find the cost of the car 2 years ago, we need to calculate the cost of the car at the time of inflation. Given: - Inflation rate = 4% per year - Current cost of the car = $30,000 - Time period = 2 years Let's calculate the cost of the car 2 years ago using the formula for inflation: \[ \text{Cost 2 years ago} = \frac{\text{Current cost}}{(1 + \text{Inflation rate})^{\text{Time period}}} \] Substitute the given values into the formula: \[ \text{Cost 2 years ago} = \frac{30000}{(1 + 0.04)^2} \] Now, let's calculate the cost of the car 2 years ago. Calculate the value by following steps: - step0: Calculate: \(\frac{30000}{\left(1+0.04\right)^{2}}\) - step1: Add the numbers: \(\frac{30000}{1.04^{2}}\) - step2: Convert the expressions: \(\frac{30000}{\left(\frac{26}{25}\right)^{2}}\) - step3: Simplify the expression: \(\frac{30000}{\frac{26^{2}}{25^{2}}}\) - step4: Rewrite the expression: \(\frac{18750000}{26^{2}}\) - step5: Reduce the fraction: \(\frac{4687500}{169}\) The cost of the car 2 years ago would have been approximately $27,736.69. Therefore, the answer is $27,736.69.