Five years ago the Phams purchased a house for $956,250. They made a down payment of 20% and took out a mortgage with TD Bank for the balance. They amortized the mortgage over 25 years at 3.45% compounded semi-annually for a 5-year term.

(a) Calculate their monthly payment. The bank rounds the payment up to the next dollar.

(b) How much interest would they pay over the 25 years assuming the same interest rate?

For the first 5 years, the Pham's paid an extra $900 per month starting with the first payment. If they continue to pay an extra $900 the entire time:

(c) How much time would it save them? (assume the interest rate stays the same)

(d) How much money would it save them?

(e) How much do they owe after making 5 years of payments (they paid the extra $900 per month starting with the first payment)?

(f) Today, when they go to renew their mortgage the interest rate has fallen to j₂= 2.5% for a five-year term. They decide to increase the size of their mortgage and use the money to pay for house renovations. They feel comfortable making a mortgage payment $5,000 per month. By increasing their mortgage, how much money will they receive to pay for house renovations if they want to pay off the mortgage over the next 20 years?