If Sandy can afford car payments of \( \$ 270 \) per month for 4 years, what is the price of a car that she can afford now? Assume an interest rate of 7.2 percent. Sandy can afford a car that costs \( \$ \square \) or Jess. \( 56.23 \%, 38.8 \) of 69 points (Round to the nearest dollar as needed.)

**Step 1. Determine the Monthly Interest Rate and the Number of Payments** - The annual interest rate is \(7.2\%\). - The monthly interest rate is \[ r = \frac{0.072}{12} = 0.006. \] - The number of payments for 4 years is \[ n = 4 \times 12 = 48. \] **Step 2. Write the Present Value of an Annuity Formula** The present value \(PV\) of an annuity (a series of equal payments) is given by \[ PV = P \times \frac{1 - (1 + r)^{-n}}{r}, \] where \(P\) is the monthly payment. Here, \(P = 270\). **Step 3. Substitute the Known Values** Substitute \(P = 270\), \(r = 0.006\), and \(n = 48\): \[ PV = 270 \times \frac{1 - (1.006)^{-48}}{0.006}. \] **Step 4. Compute \((1.006)^{-48}\)** First, compute \((1.006)^{48}\). Using logarithms: \[ \ln(1.006) \approx 0.005976, \] so \[ 48 \times 0.005976 \approx 0.28685, \] and then \[ (1.006)^{48} \approx e^{0.28685} \approx 1.33263. \] Now take the reciprocal: \[ (1.006)^{-48} = \frac{1}{1.33263} \approx 0.75056. \] **Step 5. Complete the Calculation** Substitute back: \[ PV = 270 \times \frac{1 - 0.75056}{0.006}. \] Calculate the numerator: \[ 1 - 0.75056 = 0.24944. \] Divide by \(0.006\): \[ \frac{0.24944}{0.006} \approx 41.5733. \] Then multiply by 270: \[ PV \approx 270 \times 41.5733 \approx 11231. \] **Final Answer** Sandy can afford a car that costs approximately \(\$11,\!231\).