Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $$850$ and has an existing customer base of $925.$ Paul plans to raise the annual fee by $6$ percent every year and expects the club membership to grow at a constant rate of $7$ percent for the next five years. The overall expenses of running the health club are $$420,000$ a year and are expected to grow at the inflation rate of $3$ percent annually. After five years, Paul plans to buy a luxury boat for $$875,000,$ close the health club, and travel the world in his boat for the rest of his life. Assume Paul has a remaining life of $30$ years after he retires and earns $7$ percent on his savings.

a$.$ How much will Paul have in his savings on the day he starts his world tour assuming he has already paid for his boat? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What is the annual amount that Paul can spend while on his world tour if he will have no money left in the bank when he dies? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

$\backslash$table$[[$a$.$ Account value at retirement$],[$b$.$ Annual withdrawal$]]$