You swap for face value today. Due to inflation, that means that when you go back in time your money is worth more. If I go back to 1980, every $20 bill will buy as much as $56.77 would today. That's a lot of savings! I might need only $45 to do the shopping that takes me $130 nowadays.

But you can't spend bills from the 2000 series in 1980. They don't look the same.