Let x be the original amount.
When the amount is increased by 20%, the new amount becomes 1.20x.
Then, 40% of the new amount is 0.40(1.20x) = 0.48x.
We know that 0.48x = 288, so we can solve for x:
x = 288 / 0.48
x = 600
Therefore, the original amount is $600.