Hi
 In General 
A = Accumulated Amount $1300
P= principal = $1000
r= annual rate = .12
n= periods per year = 2
t= years =

Question States
(1.06)^2t = 1300/1000
solving for t:

            2t =      
            2t = 4.50
             t = 2.25 yrs  0r 2years and 3mos.
Answer Can be verified with any of the online compound interest calculators.           
Wish You the Best in your Studies.

A(t) = ,  where P is the principal  and  n is the number of compound periods.


1300 = 


 = 


1.3 = 


log(1.3) = n*log(1.06)


n =  = 4.5  (approximately).


In order for the solution MAKES SENSE, it must be rounded to the NEAREST GREATER integer value
(to have INTEGER NUMBER of compounds).


THEREFORE, the correct  ANSWER  is 5 semi-annual compounding periods,

which is 2.5 years.