If Sandy can afford car payments of \( \$ 270 \) per month for 4 years, what is the price of a car that she can allord now? Assume an interost rate of 72 percent HW Score: \( 66.23 \%, 30.8 \) of 69 points Sandy can afford a car that costs \( \$ \square \) or less. (Round to the nearest dollar as needed.)

We first note that Sandy makes monthly payments of \( \$270 \) for 4 years. Our goal is to find the present value (price of the car) that can be afforded now. 1. Define the given values: - Monthly payment: \( P = 270 \) - Total number of payments: \( n = 4 \text{ years} \times 12 \text{ months/year} = 48 \) - Annual interest rate: \( 72\% \) - Monthly interest rate: \[ r = \frac{72\%}{12} = \frac{0.72}{12} = 0.06 \] 2. The present value of an annuity formula is: \[ PV = P \times \frac{1 - (1+r)^{-n}}{r} \] 3. Substitute the given values: \[ PV = 270 \times \frac{1 - (1.06)^{-48}}{0.06} \] 4. Compute \((1.06)^{-48}\): - First, calculate \((1.06)^{48}\). - Using logarithms or a calculator, one finds approximately: \[ (1.06)^{48} \approx 16.398 \] - Thus, \[ (1.06)^{-48} \approx \frac{1}{16.398} \approx 0.0610 \] 5. Now plug this value back into the formula: \[ PV = 270 \times \frac{1 - 0.0610}{0.06} \] Simplify the numerator: \[ 1 - 0.0610 = 0.9390 \] So we have: \[ PV = 270 \times \frac{0.9390}{0.06} \approx 270 \times 15.65 \] 6. Multiply to get the present value: \[ 270 \times 15.65 \approx 4225.5 \] 7. Rounding to the nearest dollar, Sandy can afford a car that costs approximately: \[ \$4226 \] Sandy can afford a car that costs \( \$4226 \) or less.