Question

Kyle Parker of Concord, New Hampshire, has been shopping for a new car for several weeks. He has negotiated a price of $38,000 on a model that carries a choice of a $2,500 rebate or dealer financing at 2 percent APR. The dealer loan would require a $1,000 down payment and a monthly payment of $649 for 60 months. Kyle has also arranged for a loan from his bank with a 4 percent APR. Use the Run the Numbers worksheet to advise Kyle about whether he should use the dealer financing or take the rebate and use the financing from the bank. Round your answer to two decimal places.

Adjusted APR (dealer financing):______ %

Kyle should use . (the dealer financing or the financing from the bank)

Answer 1

To advise Kyle on whether he should use the dealer financing or take the rebate and use the financing from the bank, we compare the costs of the two options. The adjusted APR for the dealer financing is 1.92%, which is lower than the financing from the bank. Therefore, Kyle should use the dealer financing option.

Step-by-step explanation:

To advise Kyle on whether he should use the dealer financing or take the rebate and use the financing from the bank, we need to compare the costs of the two options. Here's how we can calculate the adjusted APR for the dealer financing and determine which option is more advantageous:

Dealer Financing:

1. Calculate the total cost of the loan from the dealer by multiplying the monthly payment by the number of months: $649 * 60 = $38,940.
2. Calculate the effective loan amount by subtracting the down payment from the negotiated price: $38,000 - $1,000 = $37,000.
3. Find the monthly interest rate by dividing the APR by 12: 2% / 12 = 0.1667%.
4. Calculate the monthly interest paid by multiplying the loan amount by the monthly interest rate: $37,000 * 0.1667% = $61.67.
5. Calculate the adjusted monthly payment by adding the monthly interest to the original monthly payment: $649 + $61.67 = $710.67.
6. Calculate the adjusted APR by dividing the adjusted monthly payment by the effective loan amount: ($710.67 / $37,000) * 100 = 1.9219%.

Bank Financing:

1. Calculate the monthly interest rate by dividing the APR by 12: 4% / 12 = 0.3333%.
2. Calculate the monthly interest paid by multiplying the loan amount by the monthly interest rate: $37,000 * 0.3333% = $123.32.
3. Calculate the adjusted monthly payment by adding the monthly interest to the original monthly payment: $649 + $123.32 = $772.32.

Based on the calculations, the adjusted APR for the dealer financing is 1.92%. Therefore, Kyle should use the dealer financing option as it offers a lower adjusted APR compared to the financing from the bank.