Hewlett$-$Packard has completed a study indicating that $$50,000$ in reduced maintenance this year $($i$.$e$.,$ year zero$)$ on one processing line resulted from improved wireless monitoring technology.

$($a$)$ If Hewlett$-$Packard considers these types of savings worth $10\%$ per year, find the equivalent value of this result after $5$ years. $(20)$

$($b$)$ If the $$50,000$ maintenance savings occurs now, find its equivalent value $3$ years earlier with interest at $20\%$ per year. $(20)$