Q$.1$ Suppose you are considering borrowing $$120,000$ to finance your dream house. The annual percentage rate is $12\%$ and payments are made monthly.

a$.$ If the mortgage has a $20-$year amortization schedule, what are the monthly payments?

b$.$ What effective annual rate would you be paying?

c$.$ How do your answers to parts a and b change if the loan amortizes over $10$ years rather than $20?$

Q$.2$ Suppose last year you took out the loan described in problem above $($part a$).$ Now interest rates have declined to $8\%$ per year. Assume there will be no refinancing fees.

a$.$ What is the remaining balance of your current mortgage after $12$ payments?

b$.$ What would be your payment if you refinanced your mortgage at the lower rate for $19$ years?