Barbara Baker owes $$75,600$ on a $9\%,150-$day note. On day $75,$ she pays $$22,680$ on the note. On day $100,$ she pays an additional $$37,800.$

Based on the U$.$S$.$ Rule, calculate the following. $($Use a $360-$day year, and round all answers to the nearest cent.$)$

$1.$ Adjusted balance after the first payment: $

$2.$ Adjusted balance after the second payment: $

$3.$ Balance at maturity: