Rajesh Sachdeva bought a Honda Civic for a price of $29,395. He put down $4,593 and financed the rest through the dealer at an APR of 8.1 percent for four years. If payments are made monthly, the effective annual rate (EAR) is          %

To calculate the Effective Annual Rate (EAR), we first need to understand the relationship between the APR (Annual Percentage Rate) and the EAR.

The formula to calculate the EAR given the APR is:

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

Where:
- $ \text{APR} = 8.1\% = 0.081 $
- $ n = 12 $ (since the payments are made monthly)

Let's plug in the values:

\[
\text{EAR} = \left(1 + \frac{0.081}{12}\right)^{12} - 1
\]

Now, we'll calculate this step by step:

1. Calculate the monthly interest rate:
   \[
   \frac{0.081}{12} = 0.00675
   \]

2. Add 1 to the monthly interest rate:
   \[
   1 + 0.00675 = 1.00675
   \]

3. Raise this value to the power of 12 (since there are 12 months in a year):
   \[
   1.00675^{12} \approx 1.08329
   \]

4. Subtract 1 to find the EAR:
   \[
   \text{EAR} = 1.08329 - 1 = 0.08329
   \]

5. Convert the EAR to a percentage:
   \[
   \text{EAR} \approx 8.329\%
   \]

So, the Effective Annual Rate (EAR) is approximately **8.329%**.

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

Here are 5 related questions you might find helpful:
1. How does the APR differ from the EAR in terms of cost to the borrower?
2. What would be the monthly payment amount for Rajesh's loan?
3. How would the EAR change if the APR were 6% instead of 8.1%?
4. Why is the EAR usually higher than the APR when payments are made more frequently than annually?
5. What factors should be considered when comparing loans with different APRs?

**Tip:** When comparing loans, the EAR is a more accurate reflection of the true cost of borrowing than the APR, especially if interest compounds more frequently than once a year.

Learn how to calculate the Effective Annual Rate (EAR) for a Honda Civic purchase based on the given APR of 8.1% and financing details. Understand the relationship between APR and EAR with a step-by-step solution. Suitable for professionals in finance and economics.

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