What is the effective annual rate (EAR)?

Question

What is the effective annual rate (EAR)?
a. The cash flows of an investment over a one year period divided by the number of times that interest is compounded during the year.

b. The ratio of the number of the annual percentage rate to the number of compounding periods per year?

c. The discount rate for an N- year time interval, where N may be more than one year or less than or equal to one year (a fraction).

d. The interest rate that would earn the same interest with annual compounding.

Is it a, b, c, or d. The wording is confusing me. Appreciate any help :)

Answer

The effective annual rate (EAR) or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.

Answer

The wording of the answers is indeed very, very confusing. EAR will give you an interest rate that factors the impact of compounding, so if the nominal interest rate is 10% then the EAR assuming a monthly compounding is 10.471%.

The formula is:
R = (1+ i / n)  ^ n &ndash; 1. 
In this formula, R is the effective annual interest rate, i equals the stated annual interest rate and n equals the compounding period (which is usually semiannually, monthly or daily).

I can only answer the question by excluding obvious things:
a) can not be as dividing the cashflows by the no of compounding periods will only give you an average cashflow per period
b) can not be as it is just dividing the nominal rate by the number of compounding periods
c) can not be, this nswer is simply non-sense in my view
d) so, logically this is the answer but is unfair as it implicitly assume that you would calculate the EAR for a loan with less than a year period compounding.

What is the effective annual rate (EAR)?

Answers (2)