We can calculate the difference in monthly payments using the given formula for the monthly payment $PMT$:

$PMT = \frac{P \left( \frac{r}{n} \right)}{1 - \left( 1 + \frac{r}{n} \right)^{-nt}}$

Where:

• $P$ is the loan amount (the principal).
• $r$ is the annual interest rate (in decimal form).
• $n$ is the number of payments per year.
• $t$ is the number of years of the loan.

New Car Calculation:

• Principal $P = 27,000$
• Annual interest rate $r = 6.47\% = 0.0647$
• Loan term $t = 4$ years
• Monthly payments, so $n = 12$

Used Car Calculation:

• Principal $P = 16,000$
• Annual interest rate $r = 7.91\% = 0.0791$
• Loan term $t = 5$ years
• Monthly payments, so $n = 12$

We will calculate the monthly payments for both cars using this formula, then find the difference.

Let me calculate that for you.The monthly payment for the new car is approximately $639.93, and the monthly payment for the used car is approximately $323.73.

The difference in monthly payments between financing the new car and the used car is approximately $316.20.

Would you like more details or have any questions about this?

Here are 5 related questions:

1. What is the total cost of financing each car over the loan period?
2. How much interest would you pay over the life of each loan?
3. How does the loan term affect the monthly payment and total interest paid?
4. What happens if you make an extra monthly payment on either car?
5. How do these financing options compare with leasing a car?

Tip: Always consider the total cost of the loan, not just the monthly payment, to get a full picture of your financial commitment.