If each year the population of the country grows by 20%

if an amount x increases by a fraction a/b then the final amount = x * (1 + a/b)^n.

here the fraction is 20/100 ,plugging in from the asnwer to see when x doubles

1 gives = 1.2x not enough
2gives = 1.44x not enough
3 gives = 1.728x not enough
4 gives = 2.0736x enoguh because x has doubled

but the question asks how many years will elapse before the population doubles..now we know that the population doubled befoe the completion of 4 years..maybe 3 years and 10 months..so the answer is 3.