Let sum invested = P for t years.
A sum will be doubled if interest = principal = P. Amount = P+P = 2p.
Amount 2P = Px[1 + (20/100)]^t
Hence [1 + (20/100)]^t = 2
or (1.21)^t = 2
LHS is greater than two when t = 4
Hence sum will be more than doubled if it is invested for 4 years.