A partially amortizing loan for $$110,000$ for $10$ years is made at $6$ percent interest. The lender and borrower agree that payments will be monthly and that a balance of $$20,500$ will remain and be repaid at the end of year $10.$ Required: a$.$ Assuming $4$ points are charged by the lender, what will be the yield if the loan is repaid at the end of year $10?$ b$.$ What must the loan balance be if it is repaid after year $4?$ c$.$ What will be the yield to the lender if the loan is repaid at the end of year $4?$