Questions: Assume the car can be purchased for 0% down for 60 months (in lieu of rebate). A car with a sticker price of 36,100 with factory and dealer rebates of 4,200 (a) Find the monthly payment if financed for 60 months at 0% APR. (Round your answer to the nearest cent.) 531.67 (b) Find the monthly payment if financed at 2.5% add-on interest for 60 months. (Round your answer to the nearest cent.) 598.13 (c) Use the APR approximation formula to find the APR for part (b). (Round your answer to one decimal place.) 4.9% (d) State whether the 0% APR or the 2.5% add-on rate should be preferred. 0% APR 2.5% add-on rate

Solution Steps

(a) To find the monthly payment for a car financed at 0% APR for 60 months, divide the total cost of the car by the number of months.

(b) To find the monthly payment for a car financed at 2.5% add-on interest for 60 months, first calculate the total interest by multiplying the principal by the interest rate and the number of years. Add this interest to the principal and then divide by the number of months.

(c) To find the APR using the approximation formula, use the formula: \[ \text{APR} \approx \frac{2 \times n \times I}{P \times (T + 1)} \] where \( n \) is the number of payments per year, \( I \) is the total interest, \( P \) is the principal, and \( T \) is the total number of payments.

The net price of the car after applying the rebates is given by: \[ \text{Net Price} = \text{Sticker Price} - \text{Rebates} = 36100 - 4200 = 31900 \]

The monthly payment when financed at \(0\%\) APR for \(60\) months is calculated as: \[ \text{Monthly Payment}_{0\%} = \frac{\text{Net Price}}{\text{Months}} = \frac{31900}{60} \approx 531.67 \]

First, calculate the total interest for \(60\) months at an add-on interest rate of \(2.5\%\): \[ \text{Total Interest} = \text{Net Price} \times \text{Interest Rate} \times \left(\frac{\text{Months}}{12}\right) = 31900 \times 0.025 \times 5 = 3987.5 \] Next, calculate the total amount to be financed: \[ \text{Total Amount} = \text{Net Price} + \text{Total Interest} = 31900 + 3987.5 = 35887.5 \] Then, find the monthly payment: \[ \text{Monthly Payment}_{2.5\%} = \frac{\text{Total Amount}}{\text{Months}} = \frac{35887.5}{60} \approx 598.12 \]

Using the APR approximation formula: \[ \text{APR} \approx \frac{2 \times n \times I}{P \times (T + 1)} \times 100 \] where \(n = 12\), \(I = 3987.5\), \(P = 31900\), and \(T = 5\): \[ \text{APR} \approx \frac{2 \times 12 \times 3987.5}{31900 \times (5 + 1)} \times 100 \approx 50.0\% \]

Final Answer