Estimated decomposition rates of common marine debris items
The truth is: It will never totally disapear. But it will break down into ever tinier and tinier particles, until there are only monomers left. And this can take hundreds of years!
The MARPOL (International Marine Pollution) rules are changing. There are more restrictions on what you can throw overboard, though plastic and oil have always been no-no's. Getting people to comply with the laws is the trick.