Suppose that you wanted to buy a house and you borrowed $400,000 from the Commonwealth Bank. The bank offered an interest rate of j12 = 4% p.a. You agreed to repay this loan with monthly payments within 30 years, the first payment occurring one month after the loan was taken out.

(a) Determine the monthly payment.

(b) After making 25 payments you lost your job and missed the 26th, 27th and 28th payments. By the time of the 29th, the payments were resumed. How big does the 29th payment have to be to return to the original repayment schedule?

(c) After making 180 payments, the interest rate increase to j12 = 7%. Determine the new size of the monthly payment so that you can still kill off the debt after 30 years as you agreed with the bank.

(d) Find the size of the partial payment. Describe and perform a sanity check on your answer.

(e) Construct an amortization table showing the last three payments (i.e two full pay- ments and a partial payment), and describe and perform a sanity check on the final outstanding principal.