Final answer:
The effective annual rate (EAR) for a car loan with a 6% APR compounded monthly is approximately 6.168%. This rate is calculated using the formula (1 + (APR/n))^n - 1, where 'n' is 12 for monthly compounding.
Step-by-step explanation:
The effective annual rate (EAR) for a car loan with a stated annual percentage rate (APR) of 6% based on monthly compounding can be found using the formula EAR = (1 + (APR/n))^n - 1, where 'n' is the number of compounding periods per year. In this case, since the compounding is monthly, 'n' would be 12. The calculation would therefore be (1 + (0.06/12))^12 - 1.
Plugging in the values, the calculation is (1 + 0.005)^12 - 1, which equals\ (1.005)^12 - 1. Completing the calculation:
EAR = (1.005)^12 - 1 ≈ 0.06168 or 6.168%
This means the effective annual rate for the car loan is about 6.168%, which is slightly higher than the stated APR due to the effect of monthly compounding.