Question

What is the difference between the annual percentage rate (APR) and the effective annual rate (EAR)? Which rate do you believe is more relevant for financial decisions and why?

Answer 1

Annual Percentage Rate also called nominal rate does not include the affects of compounding. It infact represents simple interest rate. This rate is quoted by banks for deposits. Auto loans and mortgage loans are represented through APR.
If monthly rate = 1% . Then APR = Monthly Rate * Number of Months in year = 1%* 12 = 12%

EAR is effective annual rate which takes into consideration the number of compounding in the period . It represents compound interest rate . It is used in credit card repayment calculation. EAR is always equal or greater than APR.
If monthly rate = 1%, then EAR =(+ monthly rate)^n-1=(1+1%)^12-1 =12.68%

EAR is more relevant than APR in decision making because it takes into consideration the number of compounding . With same APR if number of compounding increases then the Future Value of the amount will increase . Semi annual compounding, Quarterly compounding or monthly compounding will have higher EAR but same APR. The actual Present value of future payment cannot be determined by APR.
EAR method is better to evaluate different loan options, mortgage loans, savings plan option because it takes into consideration the number of compounding and helps to plan better.