Suppose that you are thinking about buying a car and have narrowed down your choices to two options. The new car option: the new car costs $25000 and can be financed with a give year loan at 6.67%. The used car option: a three year old model of the same car costs $18000 and can be financed with a four year loan at 6.29%. What is the different in monthly payments between financinf the new car and financing the used car? Use PMT=P(r/n)/[1-(1+r/n)^nt]. Round your answers to the nearest cent as needed.

We can calculate the monthly payments for both the new car and the used car using the provided loan formula:

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

Where:
- $ P $ is the principal loan amount (cost of the car),
- $ r $ is the annual interest rate (in decimal form),
- $ n $ is the number of payments per year (12, for monthly payments),
- $ t $ is the number of years for the loan term.

### 1. **New Car Calculation:**
- $ P = 25000 $ (cost of the new car),
- $ r = 6.67\% = 0.0667 $,
- $ n = 12 $ (monthly payments),
- $ t = 5 $ (loan duration for 5 years).

Let's calculate the monthly payment for the new car.

### 2. **Used Car Calculation:**
- $ P = 18000 $ (cost of the used car),
- $ r = 6.29\% = 0.0629 $,
- $ n = 12 $ (monthly payments),
- $ t = 4 $ (loan duration for 4 years).

We will calculate the monthly payment for the used car as well. Then, we can find the difference between the two payments.

Let me calculate that for you.The monthly payments for the cars are as follows:
- **New car**: \$491.15 per month
- **Used car**: \$425.13 per month

The difference in monthly payments between financing the new car and financing the used car is **\$66.02**.

Do you want further details or have any questions?

Here are 5 related questions you might consider:
1. How much will the total cost of the new car be after financing?
2. How much interest will you pay over the life of the loan for both cars?
3. What happens if you extend the loan terms? How would that affect monthly payments?
4. Is it better to make a larger down payment to reduce the principal?
5. How would different interest rates affect the total cost of each car?

**Tip**: When comparing loan options, always consider both the interest rate and loan term, as a lower rate or shorter term can significantly reduce the total cost.

Suppose that you are thinking about buying a car and have narrowed down your choices to two options. The new car option: the new car costs $25000 and can be financed with a five-year loan at 6.67%. The used car option: a three-year-old model of the same car costs $18000 and can be financed with a four-year loan at 6.29%. What is the difference in monthly payments between financing the new car and financing the used car? Use PMT=P(r/n)/[1-(1+r/n)^nt]. Round your answers to the nearest cent as needed.

Compare the monthly payments for a new car ($25,000, 5-year loan at 6.67%) versus a used car ($18,000, 4-year loan at 6.29%) using the loan amortization formula. This detailed breakdown will help you understand the difference in payments, making it easier to decide which option suits your budget.

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