Background information: A young woman just had her first baby and wants to save money for their child$$s college education. The cost of college is currently $$20,000$ per year. Historically, the cost of college has increased at a rate of $6\%$ per year. Assume the first college payment is made at the start of year $19($i$.$e$.$ immediately after the child$$s $18$th birthday$).$

Round your answer to two decimal places, in dollars!$($e$.$g$.$ $$76543\mathrm{.}21)$

$1.)$ Assuming the cost of college increases an average of $6\%$ per year, how much will the first college payment be$?$

$2.)$ Assuming the account the college savings are invested in pays $8\%$ interest, then what is the amount of money she will need to have at age $18$ to pay for all four years of her child's undergraduate college education? $3.)$ What is the amount of money she needs to save every year until her child$$s $18$th birthday to achieve her goal, assuming they make her first savings payment on their child$$s first birthday, the last one on her $18$th birthday? Assume they save the same amount every year.