Michael and John are buying a house that costs $500,000. In setting up their mortgage with the bank they agree on the following payment schedule: an initial down payment, monthly payments (at the end of each month) of $1100 for 25 years, and a "pre-payment" or one time lump sum payment of $75,000 in 8 years. The loan's interest rate is 4.2% nominal annual rate compounded monthly. What down payment is required