Megan takes out a car loan for $13,000. She intends to make monthly payments for 5 years to pay off her loan. If the bank charges her an annual interest rate of 4.2% computed monthly on the loan balance, how much will her monthly payments be?

To calculate Megan’s monthly payment, we can use the **loan amortization formula**:

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

where:
- $M$ = Monthly payment  
- $P$ = Loan amount (principal) = $13,000  
- $r$ = Monthly interest rate = $ \frac{4.2\%}{12} = \frac{0.042}{12} \approx 0.0035 $  
- $n$ = Total number of payments = $5 \times 12 = 60$  

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### Step 1: Substitute values into the formula:
\[
M = \frac{13,000 \cdot 0.0035}{1 - (1 + 0.0035)^{-60}}
\]

---

### Step 2: Simplify step-by-step

\[
1 + 0.0035 = 1.0035
\]

\[
(1.0035)^{-60} \approx 0.835645
\]

\[
1 - 0.835645 = 0.164355
\]

Now:

\[
\frac{13,000 \cdot 0.0035}{0.164355} = \frac{45.5}{0.164355} \approx 276.74
\]

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### Final Answer:
Megan's monthly payment will be approximately:

\[
\boxed{276.74} \, \text{dollars}
\]

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Would you like me to break down any part of the process further or show how the interest accumulates over time?

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**5 Related Questions:**
1. How much total interest will Megan pay over the life of the loan?
2. What will be the remaining loan balance after 3 years?
3. How does the monthly payment change if the interest rate is reduced to 3%?
4. What happens if Megan makes extra payments toward the principal?
5. How much would Megan save in interest if she paid the loan off in 4 years instead of 5?

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**Tip:** Always compare loans with different interest rates and terms to understand how much you’ll pay in total interest over time.

Learn how to calculate the monthly payments for a $13,000 car loan over 5 years with a 4.2% annual interest rate, using the loan amortization formula. Step-by-step breakdown provided, suitable for students in Grades 10-12.

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