Jim plans to pay off a $450,000 loan in 15 years. To achieve this goal, he makes equal payments at the end of each fortnight based on an annual nominal interest rate of r (26) = 4.5%. (a) [4 marks] Show that the size of these fortnightly payments is $1,587.71. (b) [7 marks] At the end of four years, Jim takes a mortgage holiday for six months. How much will his fortnightly payments now change by so he can still pay off the loan in the original 15 years? (c) [6 marks] Suppose at the end of seven years, the annual nominal interest rate drops to r(26) = 3.25%. How much can Jim now top up his loan by, so to enable the original loan to be still paid off in 15 years while paying $1,587.71 per fortnight?

1. [Total: 17 marks] Jim plans to pay off a $450,000 loan in 15 years. To achieve this goal, he makes equal payments at the end of each fortnight based on an annual nominal interest rate of r(26) = 4.5%. (a) [4 marks] Show that the size of these fortnightly payments is $1,587.71. (b) [7 marks] At the end of four years, Jim takes a mortgage holiday for six months. How much will his fortnightly payments now change by so he can still pay off the loan in the original 15 years? (c) [6 marks] Suppose at the end of seven years, the annual nominal interest rate drops to r(26) = 3.25%. How much can Jim now top up his loan by, so to enable the original loan to be still paid off in 15 years while paying $1,587.71 per fortnight