You want to purchase a car. It costs 25,000. You have 3,000 that you have saved up for a down payment. You can go with the 5 year car and 60 month car loan. The car manufacture is offering a special deal on your car. You can get zero percent financing or 2,000 cash back. If you choose the cash back, the interest rate is 10 percent. If you choose the cash back, you use the cash to increase your down payment, so the amount that you have to finance is less. Which is a better deal and by how much?

Question

You want to purchase a car. It costs 25,000. You have 3,000 that you have saved up for a down payment. You can go with the 5 year car and 60 month car loan. The car manufacture is offering a special deal on your car. You can get zero percent financing or 2,000 cash back. If you choose the cash back, the interest rate is 10 percent. If you choose the cash back, you use the cash to increase your down payment, so the amount that you have to finance is less. Which is a better deal and by how much?

Answer 1

60month. by $200

Answer 2

To determine which is a better deal, we need to compare the total cost of financing under each option.

Let's start by calculating the cost of financing with the zero percent financing option:

1. Down payment: $3,000
2. Amount financed: $25,000 (car price) - $3,000 (down payment) = $22,000
3. Number of monthly payments: 60 months
4. Monthly payment: $22,000 / 60 = $366.67
5. Total cost of financing: $366.67 * 60 = $22,000

Now let's calculate the cost of financing with the cash back option:

1. Down payment: $3,000 + $2,000 (cash back) = $5,000
2. Amount financed: $25,000 (car price) - $5,000 (increased down payment) = $20,000
3. Number of monthly payments: 60 months
4. Interest rate: 10%

To calculate the monthly payment with the cash back option, we need to use a loan repayment formula. The formula is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ -Number of Months)

First, let's convert the annual interest rate to a monthly interest rate:

Monthly Interest Rate = 10% / 12 = 0.0083333

Using this information, we can now calculate the monthly payment:

Monthly Payment = ($20,000 * 0.0083333) / (1 - (1 + 0.0083333) ^ -60)
Monthly Payment ≈ $422.17

Total Cost of financing = $422.17 * 60 = $25,330.20

Now we can compare the total cost of financing under each option:

- Zero percent financing option: $22,000
- Cash back option: $25,330.20

Based on these calculations, the zero percent financing option is a better deal as it has a lower total cost of financing by approximately $3,330.20.