To find the difference in monthly payments between financing the new car and the used car, we will use the formula provided:

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

where:

• $P$ is the principal (loan amount),
• $r$ is the annual interest rate,
• $n$ is the number of payments per year (12 for monthly payments),
• $t$ is the loan term in years.

Let's calculate each option separately.

1. New Car Calculation

• Principal $P$ = 27,000
• Interest Rate $r$ = 6.67% or $0.0667$
• Loan Term $t$ = 5 ) years
• Payments per Year $n = 12$

Plugging these values into the formula, we get:

$\text{PMT}_{\text{new}} = \frac{27000 \left( \frac{0.0667}{12} \right)}{1 - \left(1 + \frac{0.0667}{12}\right)^{-12 \times 5}}$

2. Used Car Calculation

• Principal $P$ = 18,000
• Interest Rate $r$ = 7.35% or $0.0735$
• Loan Term $t$ = 4 ) years
• Payments per Year $n = 12$

Plugging these values into the formula, we get:

$\text{PMT}_{\text{used}} = \frac{18000 \left( \frac{0.0735}{12} \right)}{1 - \left(1 + \frac{0.0735}{12}\right)^{-12 \times 4}}$

I'll calculate these values for you.The monthly payments are as follows:

• New car monthly payment: $530.44
• Used car monthly payment: $433.96
• Difference in monthly payments: $96.48

Therefore, the difference in monthly payments between financing the new car and financing the used car is $96.48.

Would you like a breakdown of how each part of the calculation was done, or do you have any other questions?

Here are some related questions to consider:

1. How does the loan term affect the monthly payment for a loan?
2. What would happen to the monthly payments if the interest rates for each option changed?
3. How does the total interest paid over the life of each loan compare?
4. What would the monthly payment be if the used car loan had the same 5-year term as the new car loan?
5. How would making a larger down payment affect the monthly payment for each option?

Tip: To reduce monthly payments, consider extending the loan term, though this may increase the total interest paid.