What is the rate at which $13,824 compounded annually grows to $20,184 in 2 years.

P = principal amount = $13,824
t = time = 2 years 
A = final amount = $20,184

 $20,184 = ($13,824)(1 + r)^2
(1 + r)^2 = $20,184/$13,824 
(1 + r)^2 = about 1.46 
1 + r =
1 + r = about 1.2 
r = 1.2 - 1 
r = 0.2 

so about 20% annually