Charlie Dew purchased a new personal watercraft on October 24, 2020 from the local marina for a cost of $5000. He was sent an invoice with the following terms: 2% discount if paid in full by November 24, 2020, otherwise the full amount is due by February 24, 2021.

(a) What is the maximum interest rate at which he could borrow to take advantage of the discount? (2 marks)

(b) Suppose Charlie can find a lender who will lend him the money he needs on November 24 at the following simple interest rates: 6% for the first 20 days, 7% for the next 20 days, 8% thereafter

How much money does Charlie have to pay back to the lender on February 24, 2021? How much money does Charlie save by borrowing from this lender? (3 marks)

(c) Instead, suppose Charlie takes out an advance from his credit card to pay cash for the boat on November 24. The credit card charges r = 12% for cash advances. The credit card calculates the interest due on the last day of every month. The credit card also requires that a minimum payment of 5% of the outstanding balance be paid on the last day of each month. Charlie will make the minimum payment each month and then pay off balance owing on February 24, 2021. What is the final balance due on February 24, 2021? How much interest is Charlie charged by the credit card company in total?