A borrower is faced with choosing between two loans. Loan A is available for $$89,000$ at $6$ percent interest for $30$ years, with $6$ points to be included in closing costs. Loan B would be made for the same amount, but for $7$ percent interest for $30$ years, with $2$ points to be included in the closing costs. Both loans will be fully amortizing.

Required:

a$.$ If the loan is repaid after $20$ years, which loan would be the better choice?

b$.$ If the loan is repaid after five years, which loan is the better choice? $($Analyze the decision with both rates at two decimal places.$)$