the formula to convert a rate is given as follows
R = ((1+i*p/t)^t/p -1 )*12/t
where
i = rate at a given compounding frequency which is 30% in our question
R = rate required =?
p = compounding months of given rate = 6 months in our case
t = compound months of required rate = 12 months in our case (because it requires annual interest rate or effective interest rate)
hence R = ((1+0.30 *6/12)^(12/6) -1)*12/12= (1+0.15)^2 -1 = 0.3225 = 32.25%
if you want to convert it to quarterly rate(3 month compounding than
R = ((1+0.30*6/12)^(3/6) -1)*12/3 = 0.07238 *4 = 0.2895 = 28.95%
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