Kim and Lee wish to borrow $200,000 from the Unity Bank as a P&I loan, in order to buy an apartment. They intend to repay the loan over 15 years with regular fortnightly payments, with the first payment being one fortnight after they take out the loan. The Unity Bank charges interest at j26 = 4.94% p.a.

1. a) Illustrate the cash flows associated with this scenario as a fully labelled timeline diagram. [2 marks]

2. b) Determine the fortnightly payment size.

   [1 mark]

When they read the loan information carefully Kim and Lee find out that because they are considered risky borrowers, they will need to pay a fortnightly Mortgage Insurance Fee (MIF) every fortnight for the first three years of their loan. The fortnightly MIF is set at 0.016% of the amount borrowed.

c) Determine the size of the fortnightly MIF.

[1 mark]

4. d) Produce a new fully labelled time line diagram for the loan repayment scenario, showing all the values, and incorporating the MIFs.

   [2 marks]

5. e) Kim and Lee want to be able to compare the loan from the Unity Bank with what is available from other banks. To do this they need to know the comparison rate. To do this they need to solve an Equation of Equivalence (EoE). This is an expression of the form PV(what you get) = PV(what you pay). Derive and present the EoE that is appropriate for this scenario. Do NOT seek to simplify the expression. NB [Hint: This is a "Price is Right" type of problem].

[3 marks]

6. f) Using an estimate of i=0.002, determine the value of the right hand side of the equation of equivalence.

   [1 mark]

7. g) Present your next two estimates of i and the corresponding value of the right hand side of the equation of equivalence. Ensure that for each of these two steps you explain why you increased or decreased the value of i.

   [2+2 = 4 marks]

8. h) Determine a value of i, for which the Left Hand Side (LHS) and Right hand Side (RHS) of the equation of equivalence vary by no more than $10.00. NB You do not need to show any working for this question part, but merely present your answer, and the values of the RHS and LHS.

   [2 marks]

9. i) Using you answer from part (h) determine the j26 comparison rate for the Unity bank loan, and proceed to express this as an effective annual (j1) rate.

   [1+2=3 marks]

Kim and Lee find out that the East-West Bank will lend them $200,000 to be paid back over 12 years as a P&I loan with no fees and charges and an interest rate of j26 = 5.105% p.a.

j) Explain whether Kim and Lee should choose the East-West loan because the interest rate is lower than the comparison rate for the Unity Bank.