This a question from an "Interest Theory" course:

8. (10 points) A loan amount of 180000 can be repaid under the following two options: Option A: The loan and all interest due will be paid at the end of 15 years from now in a sin- gle lump sum at an effective annual interest rate of i. You are given that the total amount of interest paid under Option A is 76904.59. Option B: The lender of the loan receives interest payments at the end of each month for 15 years from now at an effective annual interest rate of i, and in addition, will receive a lump-sum repayment of the principal along with the last interest payment. The borrower will pay the monthly interest to the lender and accumulate the loan amount by making monthly deposits at the end of each month to a sinking fund for 15 years from now. For the first 12 years, the deposits are of amount K each and then, each monthly deposit is K more than the prior monthly deposit for the next 3 years. The effective monthly interest rate on the sinking fund is 0.0016. Calculate K and the total amount of net interest paid by the borrower in the first three years under Option B. 8. (10 points) A loan amount of 180000 can be repaid under the following two options: Option A: The loan and all interest due will be paid at the end of 15 years from now in a sin- gle lump sum at an effective annual interest rate of i. You are given that the total amount of interest paid under Option A is 76904.59. Option B: The lender of the loan receives interest payments at the end of each month for 15 years from now at an effective annual interest rate of i, and in addition, will receive a lump-sum repayment of the principal along with the last interest payment. The borrower will pay the monthly interest to the lender and accumulate the loan amount by making monthly deposits at the end of each month to a sinking fund for 15 years from now. For the first 12 years, the deposits are of amount K each and then, each monthly deposit is K more than the prior monthly deposit for the next 3 years. The effective monthly interest rate on the sinking fund is 0.0016. Calculate K and the total amount of net interest paid by the borrower in the first three years under Option B