No they don't. They put it into assets, which have a limited supply. This is the cause of house price inflation, and many other forms of asset inflation. This impoverishes everyone else because the rest of us simply can't compete for these assets against people who effectively have an unlimited supply. So it ends up with the wealthy owning all the assets then renting them back to the people who actually need them. This helps keep wages down because people need to work to pay these rents and so can't afford to withhold their labour. And so the cycle continues, the wealthy get even more of the available wealth,m and the rest of us suffer.
This is the inevitable result of Neoliberal, or more accurately named Neofeudal, economics. Post 1945 Governments were providing increasing amounts of the essential services, including housing, and this held prices down and kept wages up. Oil cartels started the reversal of this by causing artificially high prices, then Neofeudal economics caused the sell-off of Government assets, and all the gains we'd made since 1945 went into reverse.