Suppose you are a bank loan manager. Your target EAR is $5\%.$ Now, you are required to offer bank loan contracts to customers.

$(1)$ If customer A wants to borrow $$1,000,000$ and to make monthly repayments for $3$ years, then what monthly payment amount should you offer?

$(2)$ If customer B wants to borrow $$1,000,000$ and to pay only interest for the first $3$ years and then make monthly repayments for the next $3$ years, then what is the offered interest for the first $3$ years and what is the monthly payment amount for the next $3$ years?

$(3)$ After one year from the loan contract date for customers A and B$,$ the current EAR becomes $3\%.$ Does customer A want to repay the old bank loan and borrow a new bank loan with the new interest rate? To deter this refinancing, what should be the early repayment fee in percentage term of the loan balance? Answer the same question for customer B$.$