You have just taken out a mortgage for $575,000, at a fixed rate of 4.75% per year, compounded monthly, and a term of 30 years.

a) Calculate the monthly payments

b) For the first six months' payments, calculate the portion that is interest and the portion that is principal

c) Immediately after the sixth payment, what is the balance remaining on the mortgage?

d) If you design the mortgage so that the payments will grow at 0.20% per month, what will be the first payment on the mortgage?