You currently owe $200,000 on your home mortgage. The APR on this loan is 6% and payments are due monthly. The value of your home has dropped to $175,000 in the last two years. Fearing that you might walk away from the loan and that he might get stuck with your property, the loan officer at the bank that owns your mortgage has offered to replace the old loan with a new loan of $150,000 and the same 6% interest rate. The only catch is that the bank would receive 50% of any future appreciation in the value of your home.

a) What monthly interest rate you are paying on your loan? What is the effective annual rate (EAR)? 

b) If the term of the new $150,000 loan is 25 years, what will be your monthly interest and principal payment (don't worry about property taxes and insurance)?

c) Suppose that you accept the offer and exactly three years (36 months) later, you sell your home for $210,000 and pay off the remainder of the $150,000 loan. What will the remaining balance of the loan be after 36 months (e.g., what will it cost to repay the remainder)?