as given stated rate = 13.5 %

let we put 1000 $ in our account

after time period of 1 yr

compound interest = (1000)(13.5)(1)/100 = 135 $

now when interest in compounded semiannually ,

after 1st semiannual i.e 6 months 

compound interest = (13.5/2)% of 1000 = 135/2 = 67.5

compounded money (say CP1) =  1000 + 67.5 = 1067.50 $

after 2nd semiannual i.e next 6 months 

compound interest =67.5 +  (13.5/2)% of 67.5 = 67.5 + 4.55 = 72.05

compounded money (say CP2) = 1067.5 + 72.05 = 1139.55 $

therefore total compound interest = 1139.55 -1000 = 139.55 $ = (1000xeffective rate)/100 

so, effective rate = 139.55/10 = 13.95 %