You are considering a $1,000,000 ARM with a 30-year amortization starting at 4.5% APR with 5/1 (5: the rate is fixed for the first 5 years and 1: adjustment period) and 3/8 (3%: periodic cap; 8%: lifetime cap). The margin is 2.75%.

a. Find the monthly payment for the first 5 years

b. Suppose that the index rate is 4.25% after 5 years. What is the interest rate for the 6th year? Find the monthly payment for the 6th year

c. At the beginning of the 7th year, the index is 8.25%. Find the new mortgage rate. Calculate the monthly payment.