ind the monthly payment necessary to amortize the following auto loan.
​$12 comma 90012,900​, 5.75.7​% ​interest; 66 years


To calculate the monthly payment necessary to amortize an auto loan, we can use the standard amortization formula:

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

Where:
- $M$ is the monthly payment.
- $P$ is the loan amount.
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the total number of monthly payments (loan term in months).

Given:
- $P = 12,900$ dollars (loan amount),
- Annual interest rate $= 5.7\%$,
- Loan term $= 6$ years.

### Step 1: Convert annual interest rate to monthly interest rate
\[
r = \frac{5.7\%}{12} = \frac{0.057}{12} \approx 0.00475
\]

### Step 2: Calculate the number of months
\[
n = 6 \times 12 = 72 \text{ months}
\]

### Step 3: Plug values into the amortization formula
\[
M = \frac{12,900 \times 0.00475 \times (1 + 0.00475)^{72}}{(1 + 0.00475)^{72} - 1}
\]

Let me calculate this.The monthly payment necessary to amortize the loan is approximately **$211.97**.

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

Here are 5 related questions you may find interesting:
1. How does the loan term affect the monthly payment amount?
2. What is the total interest paid over the life of the loan?
3. How does an increase in the interest rate impact the monthly payment?
4. Can an extra payment each month reduce the total interest paid?
5. How would the monthly payment change if the loan term were shorter (e.g., 4 years instead of 6)?

**Tip**: Increasing the loan term reduces your monthly payments but increases the total interest you will pay over time.

Find the monthly payment necessary to amortize the following auto loan: $12,900, 5.7% interest; 6 years.

Learn how to calculate the monthly payment for a $12,900 auto loan with 5.7% interest over a 6-year term. This guide walks you through the loan amortization formula and includes step-by-step calculations. Suitable for high school students in Grades 11-12.

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