For Real Estate Investments:

John decides to buy a house that costs $750,000. For that purpose, John uses an 85% Loan to Value mortgage. He gets got a 30-year, 3/1 ARM with an initial rate of 3.75%. The reset margin on the mortgage is 3% above the index (1-year CMT). The index was 1% at the origination date, but John predicts that the index will become 3.50% after the first reset. John needs also to pay 3 points in order to get this mortgage

a. What is John's monthly payment during the first 3 years?

b. Assuming that John's predictions become true, what will be his new monthly mortgage payment in the fourth year?

c. Assuming that John's predictions were wrong and the index remains 1% for the life of the mortgage, find its true APR.

Please include all steps to these processes with calculations from calculator. Thank you! :)