As the number of compounding period increases annual percentage rate (APR) remains same

Explain this concept, I am not getting this

EAR = Effective Annual Rate, APR=Annual Percentage Rate

Look at this… 4% compounding annual. APR = 4%, EAR=4%

4% compounded semi-annual -> 1.02^2 = 1.0404 => EAR=4.04%, APR = 2% * 2 = 4%

4% compounded quarterly -> EAR => 1.01^4 => 1.040606 => EAR= 4.0604% But APR = 1% x 4 = 4%

APR is always 4% per year, but EAR changes - and inceases as the number of times the compounding occurs.

The APR is the way someone tries to tell you that the rate is lower – but what you actually end up paying is the EAR … which is higher.

So someone will tell you - you will be paying 10% APR - but if you are paying monthly -> you would be paying (1+.1/12) ^ 12 = 10.47%.

APR is a nominal rate, not an effective rate.

I wrote an article on nominal versus effective rates that may be of some help here:

You should look at the difference betwen Effective Annual Rate, which is affected by the compounding period, and the Annual Percentage Rate, which isn’t. Particularly, look at pages 287 - 289 of the Quanatative Methods book.

Think of the APR as a pie that can be sliced into as many pieces as you want… No matter how many slices (compounding periods) you divide it into, the size of the pie doesn’t change.

The EAR is different. That is equivilant annual rate is where you look at the effect of all of your compounding over the course of the year and describe that as if there was a single rate applied for the whole year. So, if you compound a bunch (e.g., daily) you will have more money at the end of the year than if you either don’t compound or compound just a little (e.g.,semi-annually) . So, the more slices, the bigger the pie gets.

Thus, your EAR will always be the same or a little higher than the APR.

Hope this helps.