Lindsey bought a new car for \( \$ 29,000 \). She paid a \( 20 \% \) down payment and financed the remaining balance for 48 months with an APR of \( 4.3 \% \). Assuming she made monthly payments, determine the total cost of Lindsey's car. Round your answer to the nearest cent, if necessary.

To determine the total cost of Lindsey's car, we need to follow these steps: 1. **Calculate the down payment**: \[ \text{Down payment} = 20\% \text{ of } 29000 = 0.20 \times 29000 = 5800 \] 2. **Calculate the financed amount**: \[ \text{Financed amount} = \text{Total cost} - \text{Down payment} = 29000 - 5800 = 23200 \] 3. **Calculate the monthly interest rate**: The APR is \( 4.3\% \), so the monthly interest rate is: \[ \text{Monthly interest rate} = \frac{4.3\%}{12} = \frac{0.043}{12} \approx 0.00358333 \] 4. **Calculate the monthly payment using the formula for an installment loan**: The formula for the monthly payment \( M \) is given by: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] where: - \( P \) is the loan amount (financed amount), - \( r \) is the monthly interest rate, - \( n \) is the number of payments (months). Plugging in the values: - \( P = 23200 \) - \( r \approx 0.00358333 \) - \( n = 48 \) \[ M = 23200 \frac{0.00358333(1 + 0.00358333)^{48}}{(1 + 0.00358333)^{48} - 1} \] First, calculate \( (1 + r)^{48} \): \[ (1 + 0.00358333)^{48} \approx 1.183682 \] Now substitute this back into the formula: \[ M = 23200 \frac{0.00358333 \times 1.183682}{1.183682 - 1} \] \[ M = 23200 \frac{0.004247}{0.183682} \approx 23200 \times 0.023141 \approx 536.27 \] 5. **Calculate the total payment over 48 months**: \[ \text{Total payment} = M \times n = 536.27 \times 48 \approx 25701.00 \] 6. **Calculate the total cost of the car**: \[ \text{Total cost} = \text{Down payment} + \text{Total payment} = 5800 + 25701.00 = 31501.00 \] Thus, the total cost of Lindsey's car is approximately \( \boxed{31501.00} \).