A mortgage loan in the amount of $$100,000$ is made at $12$ percent interest for $20$ years. Payments are to be monthly in each part of this problem.

a$.$ What will the loan balance be at the end of year $5$ if the loan is fully amortizing?

b$.$ What would be the interest portion of the payment scheduled for payment at the end of month $61$ if the loan is fully amortizing?

c$.$ Assume that the lender charges $3$ points to close the loans. What would be the effective rate of interest?