If inflation has been running at \( 2.93 \% \) per year and a new car costs \( \$ 10,700 \) today, what would it have cost 2 years ago? A car that costs \( \$ 10,700 \) today would have cost \( \$ \square 2 \) years ago. (Do not round until the final answer. Then round to the nearest cent as needed.)

To find the cost of the car 2 years ago given the current price and the inflation rate, we can use the formula for calculating the present value based on inflation: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \( PV \) is the present value (the cost of the car 2 years ago), - \( FV \) is the future value (the current cost of the car, which is \( 10,700 \)), - \( r \) is the inflation rate (expressed as a decimal, so \( 2.93\% = 0.0293 \)), - \( n \) is the number of years (which is \( 2 \) in this case). Now, we can substitute the values into the formula: \[ PV = \frac{10,700}{(1 + 0.0293)^2} \] Let's calculate this step by step. First, we will calculate \( (1 + 0.0293)^2 \) and then use it to find \( PV \). I'll perform the calculations now. Calculate the value by following steps: - step0: Calculate: \(\left(1+0.0293\right)^{2}\) - step1: Add the numbers: \(1.0293^{2}\) - step2: Convert the expressions: \(\left(\frac{10293}{10000}\right)^{2}\) - step3: Use the properties of exponents: \(\frac{10293^{2}}{10000^{2}}\) Calculate or simplify the expression \( 10700 / 1.05945849 \). Calculate the value by following steps: - step0: Calculate: \(\frac{10700}{1.05945849}\) - step1: Convert the expressions: \(\frac{10700}{\frac{105945849}{100000000}}\) - step2: Multiply by the reciprocal: \(10700\times \frac{100000000}{105945849}\) - step3: Multiply: \(\frac{10700\times 100000000}{105945849}\) - step4: Multiply: \(\frac{1070000000000}{105945849}\) Now that we have calculated the necessary values, we can summarize the steps: 1. We calculated \( (1 + 0.0293)^2 \) which is approximately \( 1.05945849 \). 2. We then used this value to find the present value (cost of the car 2 years ago): \[ PV \approx \frac{10,700}{1.05945849} \approx 10,099.499037 \] Finally, rounding to the nearest cent, the cost of the car 2 years ago would have been approximately: \[ PV \approx 10,099.50 \] Thus, a car that costs \( \$ 10,700 \) today would have cost \( \$ 10,099.50 \) 2 years ago.