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 ​$27 comma 000 and can be financed with a four​-year loan at 6.47​%.
The​ used-car option: A​ three-year old model of the same car costs ​$16 comma 000 and can be financed with a five​-year loan at 7.91​%.
What is the difference in monthly payments between financing the new car and financing the used​ car? Use PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction
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Part 1
The difference in monthly payments between financing the new car and financing the used car is ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)

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.

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 $27,000 and can be financed with a four-year loan at 6.47%. The used-car option: A three-year-old model of the same car costs $16,000 and can be financed with a five-year loan at 7.91%. What is the difference in monthly payments between financing the new car and financing the used car?

Learn how to calculate the difference in monthly payments between financing a new car ($27,000 at 6.47%) and a used car ($16,000 at 7.91%). This problem includes loan payment calculations using finance math concepts and detailed step-by-step formulas.

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