A homeowner has obtained a $600,000 mortgage from a local bank. The mortgage is repayable via level monthly instalments (covering both the principal and interest) in arrears over a period of 25 years. The interest charged is calculated at 4% per annum convertible monthly. After 6 years and 7 months, the interest rate is increased to 5% per annum convertible monthly. Consequently, the term of the loan is lengthened while the size of the instalments remains unchanged except for the very last instalment which is smaller than the previous instalment amount. a. Calculate the new term of the loan outstanding at 6 years and 7 months (i.e. after the interest rate change), in terms of the complete number of months. (10 marks) b. Calculate the new amount of the very final instalment after the interest rate change. (2 marks)