please show all steps and do not solve using excel

2. Your local gift shop starts a membership program for its loyal customers. Customers who have 5-year membership card will get 10% discount on every purchase and the store owner believes that a loyal customer spends $180 (before discount) on average in the store every year. The market interest rate is 7%. a. If the store owner's expectations are correct, how much can he 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 10% discount on every purchase again but they benefit from this discount forever. The owner believes that those who want this card also spend $180 (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