How I understood EAR & apr

We know

1 + EAR =  ( 1+ APR/x )^x

Example:- 100 bond 5% coupon seminannual payments . Current price 957.35

Compute Rate  =ZINS(10;25;-957,35;1000) = 3%

3%

So APR = 6%
EAR = 6.09%

How ?

APR is computed like Simple interest so semiannualy in this ques.
Both APR and EAR are expressed in annual terma´s


957.35(1.03)(1.03) = 1015.652615

EAR
957.35(1 + ear) = 1015.652615
957.35 + 957.35*ear = 1015.652615
 957.35*ear = 1015.652615 - 957.35
ear  = 58,302615/957.35

ear = 0,0609

Just the compounded % of how much u earned ! 

= HOW MUCH U EARNED PER YR / INITIAL MONEY

Now see the first equation and see this 

957.35(1.03)^2= 1015.652615

(1.03)^2= 1015.652615/957.35      =  1+rate = (1 + ear)1/2   /* This is the imp. point to understand because compounded semianually*/

So half of the ear return  is the apr return per 6 months.

Thats all folks :)



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