You want to buy a new sports coupe for $74,100, and the finance office at the dealership has quoted you a loan with an APR of 6.5 percent for 36 months to buy the car.

What will your monthly payments be?

Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.

What is the effective annual rate on this loan?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

### Step 1: Calculating Monthly Payments

The formula for the monthly payment on a loan is:

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

Where:
- $ P $ = Principal loan amount (the price of the car) = \$74,100
- $ r $ = Monthly interest rate = $\frac{APR}{12}$
- $ n $ = Total number of payments = 36 (since it's a 36-month loan)

The annual interest rate (APR) is 6.5%, so the monthly interest rate is:

\[
r = \frac{6.5\%}{12} = \frac{0.065}{12} \approx 0.00541667
\]

Now, using the formula, we can calculate the monthly payment.

### Step 2: Calculating Effective Annual Rate (EAR)

The formula for the Effective Annual Rate (EAR) is:

\[
EAR = \left( 1 + \frac{APR}{12} \right)^{12} - 1
\]

Now, I will calculate both the monthly payment and the EAR.### Results:

- **Monthly Payment**: \$2,271.09
- **Effective Annual Rate (EAR)**: 6.70%

Would you like further details on the calculations or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the monthly payment change if the loan term was extended to 48 months?
2. What would happen to the effective annual rate (EAR) if the APR were lower?
3. How would a larger down payment affect the monthly payments and the total loan cost?
4. What would the monthly payments be if the interest rate were compounded daily instead of monthly?
5. How does the APR compare to the actual interest paid over the term of the loan?

**Tip:** Understanding the difference between the nominal interest rate (APR) and the effective annual rate (EAR) helps in comparing loan offers!

You want to buy a new sports coupe for $74,100, and the finance office at the dealership has quoted you a loan with an APR of 6.5 percent for 36 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?

Find out how to calculate monthly payments and the effective annual rate (EAR) for a car loan of $74,100 at 6.5% APR over 36 months. Learn about loan amortization, interest rates, and the difference between APR and EAR with a detailed step-by-step solution.

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