A partially amortizing loan for $$103,000$ for $10$ years is made at $5$ percent interest. The lender and borrower agree that payments will

be monthly and that a balance of $$20,000$ will remain and be repaid at the end year $10.$

Required:

a$.$ Assuming $3$ 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 $4?$

Note: For all requirements, do not round intermediate calculations, round your final answers to $2$ decimal places.