Questions: Christina bought a new car for 31,000. She paid a 10% down payment and financed the remaining balance for 48 months with an APR of 4.5%. Determine the monthly payment that Christina pays. Round your answer to the nearest cent, if necessary.

Solution Steps

The down payment is calculated as follows: \[ \text{Down Payment} = \text{Total Cost} \times \text{Down Payment Rate} = 31000 \times 0.10 = 3100 \]

The financed amount is determined by subtracting the down payment from the total cost: \[ \text{Financed Amount} = \text{Total Cost} - \text{Down Payment} = 31000 - 3100 = 27900 \]

The monthly interest rate is derived from the annual interest rate: \[ \text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12} = \frac{0.045}{12} = 0.00375 \]

Using the loan payment formula, the monthly payment is calculated as follows: \[ \text{Monthly Payment} = \frac{\text{Financed Amount} \times \text{Monthly Interest Rate}}{1 - (1 + \text{Monthly Interest Rate})^{-\text{Loan Term in Months}}} \] Substituting the values: \[ \text{Monthly Payment} = \frac{27900 \times 0.00375}{1 - (1 + 0.00375)^{-48}} \approx 636.22 \]

Final Answer