Luke is buying a house. The price is $500,000. The down payment required by the bank is $100,000 (20% of the purchase price.) For the remaining balance of $400,000, the bank offers Luke a 30 year mortgage at a rate of 6% p.a. monthly compounding. 

What is the monthly payment Luke has to send to the bank every month over the next 30 years?

 

A second bank offers Luke a 15-year mortgage at a rate of 5% p.a., monthly compounding. This bank asks for a $125,000 down payment. 

Which offer is optimal for Luke, assuming his opportunity cost of capital is 8% p.a. monthly compounding?