Your local gift shop starts a membership program for its loyal customers. Customers who have $5$year membership card will get $15\%$ discount on every purchase and the store owner believes that a loyal customer spends $$135($before discount$)$ on average in the store every year. The market interest rate is $5\%.$

a$)$ If the store owner's expectations are correct, how much can she charge for the $5-$year membership card? $($Note: Assume the customers make all their purchases at the end of the year.$)$

b$)$ The owner also introduces another type of membership program: A perpetual membership. Customers who own this type of membership card get $15\%$ discount on every purchase again but they benefit from this discount forever. The owner believes that those who want this card also spend $$135($before discount$)$ annually. If this is the case, what will be the price difference between the $5-$year membership card and the perpetual membership card?