A borrower takes-out a partially amortizing loan in the amount of $80,000 for 30 years at 4% APR, compounded monthly. A balance of $20,000 will remain and be paid as a lump sum when the term of this loan expires. (a) What is the outstanding balance of the loan after 10 years?

(b) After 10 years, the borrower decides to make a large payment of $10,000 to the lender. What are the new monthly payments the borrower must make after payment of the $10,000?