Palmer Frosted Flakes Company offers its customers a pottery cereal bowl if they send in $3$ boxtops from Palmer Frosted Flakes boxes and $$1.$ The company estimates that $60\%$ of the boxtops will be redeemed. In $2018,$ the company sold $1,350,000$ boxes of Frosted Flakes and customers redeemed $660,000$ boxtops receiving $220,000$ bowls. If the bowls cost Palmer Company $$3$ each, how much liability for outstanding premiums should be recorded at the end of $2018?$