What is the largest possible value of coins is it possible to have without having any coins which will add to 4 dollars coins are 5c 10c 20c 50c 1 dollar 2 dollar?

Tentatively I will say $4.35, with for instance: 19 x 20c 1 x 50c 1 x 5c It's possible that a rigorous method exists, but this is just a fudged guess. Any advances on it?