For questions #$7-10,$ the periodic rate is $2\%.$

Pete has a charge account at Art's Supplies. The finance charge is computed using the average$-$daily$-$balance method where new purchases are not included. Pete's previous balance is $$145\mathrm{.}00,$ and the billing period is from April $1-$April $30.$ On April $10,$ Pete made a $$50\mathrm{.}00$ payment. On April $20,$ he made a purchase of $$63\mathrm{.}45.$ What is his average daily balance? What is his finance charge? What is his new balance?