Best threshold for a d20 roll-or-cash game

You have $100$ moves and a fair $20$-sided die whose top face currently shows $1$. Each move is either a roll, which re-randomises the top face, or a take, which pays you the number currently on top in dollars without ending the game; takes do not require a roll in between (so taking $100$ times immediately guarantees $100). You commit in advance to this plan: roll until the top face is at least $n$ for the first time, then take on every remaining move. Choosing $n$ optimally, what is the expected payout?

$5320/3\approx 1773.33$ dollars. With threshold $n$ the face you lock in averages $\tfrac{20+n}{2}$ and reaching it takes on average $\tfrac{20}{21-n}$ rolls, leaving about $100-\tfrac{20}{21-n}$ takes. The product is maximised at $n=18$: $19\cdot(100-\tfrac{20}{3})=\tfrac{5320}{3}$.