You are going to buy a condo apartment for $800,000. You will pay $200,000 up front and then borrow the remaining $600,000 from a bank. You will pay back the loan over 30 years in equal payments using a nominal rate of 6%. Payments are due at the end of every month.

a) What is the effective annual interest rate?

b) What is the monthly payment?

c) Suppose that exactly five years have passed and the interest rates are now 5% and you decided to re-finance your loan in which you have to pay the remaining portion of the principal on the loan to the bank. Exactly how much do you owe the bank at that point?