Five years ago, you took out a 25-year mortgage with monthly payments and a quoted APR of 2:5% (with semi-annual compounding) for $400; 000:

(a) Find the eective monthly interest rate and the initial monthly mortgage payment (for the rst 5 years of the mortgage). Find how much of the mortgage has been reimbursed and how much remains after 5 years.

(b) You have just received a promotion and a bonus of $100; 000 and would like to pay part of your mortgage in order to reduce your monthly payments. What will be your new monthly payments for the rest of the mortgage term assuming the interest rate stays the same? Draw the timeline. Show your work