Harper is considering the purchase of a ​$9 comma 298 used car and is trying to decide between a 48​-month and a 60​-month car loan. If the loan is for ​$9 comma 298 at 5 ​percent, what is the difference in the monthly​ payments?
​Note: Round intermediate computations to at least five​ (5) decimal places.
Click on the table icon to view the Monthly Installment Loan Payment Factor​ (MILPF) table: LOADING....
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Part 1
The monthly payment for the 48​-month car loan is ​$

enter your response here.  ​(Round to the nearest​ cent.)
Part 2
The monthly payment for the 60​-month car loan is ​$

enter your response here.  ​(Round to the nearest​ cent.)
Part 3
The difference between the monthly payments is ​$

enter your response here.  ​(Round to the nearest​ cent.)

To find the monthly payments for both the 48-month and 60-month loans, we need to use the formula for monthly loan payments, which is derived from the amortization formula:

\[
M = \dfrac{P \cdot r}{1 - (1 + r)^{-n}}
\]

Where:
- $M$ = Monthly payment
- $P$ = Loan amount ($9,298)
- $r$ = Monthly interest rate (annual rate divided by 12)
- $n$ = Total number of payments (loan term in months)

We are given:
- Loan amount $P = 9,298$
- Annual interest rate $5\%$ or $0.05$

Thus, the monthly interest rate $r = \dfrac{5\%}{12} = 0.004167$.

### Part 1: Monthly Payment for the 48-month Loan
For a 48-month loan, $n = 48$:

\[
M_{48} = \dfrac{9,298 \cdot 0.004167}{1 - (1 + 0.004167)^{-48}}
\]

I'll compute this next.

### Part 2: Monthly Payment for the 60-month Loan
For a 60-month loan, $n = 60$:

\[
M_{60} = \dfrac{9,298 \cdot 0.004167}{1 - (1 + 0.004167)^{-60}}
\]

### Part 3: Difference in Monthly Payments
Once we have both monthly payments, the difference is simply:

\[
\text{Difference} = M_{48} - M_{60}
\]

I’ll calculate the results for you now.### Results:

1. **Monthly payment for the 48-month car loan**: \$214.13 (rounded to the nearest cent)
2. **Monthly payment for the 60-month car loan**: \$175.46 (rounded to the nearest cent)
3. **Difference between the monthly payments**: \$38.66 (rounded to the nearest cent)

Would you like more details or have any further questions?

Here are five related questions to deepen understanding:
1. How would increasing the interest rate affect the monthly payments?
2. What is the total interest paid over the life of both the 48-month and 60-month loans?
3. How would a larger down payment impact the monthly payments?
4. What would be the monthly payments if the loan term was 36 months instead?
5. How does the principal paid off in each month change over time in both loans?

**Tip**: Longer loan terms usually result in lower monthly payments but higher total interest paid over time.

Harper is considering the purchase of a ​$9,298 used car and is trying to decide between a 48​-month and a 60​-month car loan. If the loan is for ​$9,298 at 5​ percent, what is the difference in the monthly​ payments?

Find out the difference in monthly payments for a $9,298 used car loan at 5% interest, comparing a 48-month and a 60-month loan term. Learn how to apply the loan amortization formula to calculate exact payments and understand key financial concepts.

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