Please show formulas not just excel

Claire is going to purchase a $400,000 home. To do so, she will make a $40,000 down payment and t out a 30-year mortgage for the remainder. The interest rate on the mortgage will be 6% per year compounded monthly. She will be 3% per year compounded yearly. ake will make monthly payments. The average inflation rate over the next 30 years (a) What is the monthly payment? (5 points) (b) How many months will it take to pay off the mortgage? (5 points) (c) How much interest will Claire pay over the life of the loan? (10 points) (d) Assume inflation will be 3% per year compounded yearly for the next 30 years. What will Claire's final payment be in real terms? (5 points)