Final answer:
For a loan with a 10% stated annual percentage rate (APR) that is compounded quarterly, the effective annual rate (EAR) is roughly 10.38%.
Step-by-step explanation:
The Effective Annual Rate (EAR) for a loan with a stated APR of 10% compounded quarterly can be calculated using the formula EAR = (1 + i/n)n - 1, where i is the annual interest rate (in this case 10% or 0.10) and n is the number of compounding periods per year.
Calculating it, we would have:
EAR = (1 + 0.10/4)4 - 1EAR = (1 + 0.025)4 - 1EAR = (1.025)4 - 1EAR ≈ 1.103812890625 - 1EAR ≈ 0.103812890625 or 10.38%
So, the EAR is approximately 10.38%, which would be the answer.