A partially amortizing mortgage is made for $$69,000$ for a term of $10$ years. The borrower and lender agree that a balance of $$21,800$ will remain and be repaid as a lump sum at that time.

Required:

a$.$ If the interest rate is $7$ percent, what must monthly payments be over the $10-$year period?

b$.$ If the borrower chooses to repay the loan after five years instead of at the end of year $10,$ what must the loan balance be$?$