Effective Annual Rate Explanation

I have already explain effective annual rate or EAR in yesterday content APR vs EAR. But, I have studied more resource and ready to explain it with more simple way.

EAR is just like a compound interest rate. We know that Compound interest is excess of amount over principal.

Compound interest = Amount - Principal.

We also know that we compound interest is also calculated on principal + old interest. For example if compound interest is 10% on $ 100 loan which is given for two years. At that time, we will calculate first year

First year interest = 100 X 10/100 X 1 =Rs. 10

Second year interest = ( 100+10) X 10/100 X 1 = 11

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Total compound interest is = $ 21

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Or

Amount = Principal ( 1+ R/100 ) ^ t 

Or

Amount = Principal ( 1 + R/ 100) ^ first year X  ( 1+ R / 100) ^ Second year X ........... No. of years

Amount = 100 ( 1+10/100)^2 = 121

Total Compound Interest = Amount - Principal

Total Compound Interest = 121 - 100 = $ 21

Now, are apply same in Effective annual percentage rate.

A credit card company has given loan of $ 1 for one year. This loan is given on the basis 0.6274% interest rate daily basis. Calculate its  Effective annual rate. Now can calculate total amount with following way

First Day Amount = $ 1

Second Day Amount = $ 1 ( 1 + 0.6274 / 100 )^ 1

Third day Amount = $ 1 ( 1+0.6274 / 100 ) ^ 1  X  ( 1 + 0.6274 / 100 )^ 1

Forth day Amount = $ 1  ( 1+0.6274 / 100 ) ^ 3

Like this 365th day Amount = $ 1  ( 1+0.6274 / 100 ) ^ 365

or

Like this 365th day Amount =  $ 1.257

Compound Interest or Effective Annual Rate = Amount - Principal  = $ 1.257 - $ 1 = $ 0.257 or 25.7%