A borrower is faced with choosing between two loans. Loan $A$ is available for $$82,000$ 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, what is the effective interest rate for Loan A and Loan $B?$

b$.$ If the loan is expected to be repaid after five years, what is the effective interest rate for Loan A and Loan B$?$