Car Loan APR: Understanding the True Cost of Borrowing

What is the effective annual rate of a car loan with a stated APR of 6.38% based on monthly compounding?

When considering a car loan with a stated APR of 6.38% that compounds monthly, how can we determine the true cost of borrowing?

Effective Annual Rate Calculation:

The effective annual rate of the car loan with a stated APR of 6.38% based on monthly compounding is approximately 6.53%. This takes into account the compounding effect over a year and provides a more accurate measure of the true cost of the loan.

To calculate the effective annual rate, we need to consider the effect of compounding. Since the loan has a stated APR based on monthly compounding, we can use the formula for the effective annual rate:

Effective Annual Rate = (1 + (Stated APR / Number of compounding periods))^Number of compounding periods - 1

In this case, the stated APR is 6.38%, and the loan compounds monthly (12 times a year).

Plugging in the values into the formula:

Effective Annual Rate = (1 + (0.0638 / 12))^12 - 1

Calculating the result:

Effective Annual Rate ≈ (1 + 0.00532)^12 - 1

Effective Annual Rate ≈ (1.00532)^12 - 1

Effective Annual Rate ≈ 1.0653 - 1

Effective Annual Rate ≈ 0.0653

Converting to a percentage:

Effective Annual Rate ≈ 6.53%

The effective annual rate of the car loan with a stated APR of 6.38% based on monthly compounding is approximately 6.53%. This calculation takes into consideration the compounding effect and provides a more accurate measure of the true cost of borrowing.