Final answer:
The effective annual rate (EAR) or EFF% is a measure of the total interest that will be earned on an investment, taking into account the effects of compounding. The EFF% for a nominal rate of 12% compounded semiannually is 12.36%. The EFF% for compounded quarterly, monthly, and daily are 12.55%, 12.68%, and 12.75% respectively.
Step-by-step explanation:
The effective annual rate (EAR) or EFF% is a measure of the total interest that will be earned on an investment, taking into account the effects of compounding. It is the actual interest rate that will be earned or paid on an investment or loan over a year, taking into account the frequency of compounding.
To calculate the EFF% for a nominal rate of 12% compounded semiannually, we use the formula: EFF% = (1 + (nominal interest rate / number of compounding periods))^(number of compounding periods) - 1. Substituting in the values, we get EFF% = (1 + (0.12 / 2))^2 - 1 = 12.36%.
Similarly, for compounded quarterly, we get EFF% = (1 + (0.12 / 4))^4 - 1 = 12.55%. For compounded monthly, EFF% = (1 + (0.12 / 12))^12 - 1 = 12.68%. And for compounded daily, EFF% = (1 + (0.12 / 365))^365 - 1 = 12.75%.