A purpose-built full-nitro .500 that is worth having will cost several multiples of that. If you find one that is fairly priced at $4,000, you don't want it. Nothing worse than a cheap double rifle.
You might be able to sneak up on a used Merkel .500 for $10k or somewhat less. They're about the minimum benchmark that I've found acceptable. The Merkel DRs are serviceable, functional rifles, but certainly don't represent an ideal. I don't pay much attention to them, so I'm guessing a little on current used prices. The Heym PH model is a very plain, "working" rifle of solid quality that is available new at $16,500 and can be ordered stocked to your dimensions. Nice used British rifles in .500 Nitro can be found, but if they're in good enough condition to be desirable at all, they'll be a lot more expensive.
