When Gloria turns $35$ years old, she will set a goal of retiring at age $60$ with $$850,000.$

$($a$)$ How much money does she need to set aside on her $35$th birthday to reach this goal, assuming her investments earn an effective annual interest rate of $10\mathrm{.}4\%?$

$($b$)$ How much would she have had to set aside if she starts $10$ years earlier?