Question 1: [18 marks] You are considering investing in a scholarship fund for your daughter. The fund operates in the following way: Starting in one month's time you would make regular monthly deposits of $50 for a period of eight years into a scholarship fund. Immediately after your final deposit the fund would pay $10,000 to your daughter to help her with expenses when she commences university study. a) Illustrate this scenario as a fully labelled time line diagram. [2 marks] To be able to compare this fund with other possible investments, you need to know the effective interest rate, ju, that this fund returns. b) Derive and present the equation of equivalence that is appropriate for this scenario. Do NOT seek to simplify the expression, but rather leave $10,000 as the value of the left hand side (LHS). (Hint: This is a "Price is Right" problem but with a FV.] [4 marks] c) Using an estimate of i=1%, determine the value of the right hand side (RHS) of the equation of equivalence. Enter this value to 2 decimal places as an answer to "Assignment 1 - Milestones" question 1c. You can have as many attempts of this as you wish without penalty, but this question will close at 4:00pm on Friday 7 August. There will be no marks available for this question part after then [2 marks] right hand side of the equation of equivalence. Ensure that for each of these d) Present you next three estimates of i and the corresponding value of three steps you explain why you increased or decreased the value of i. [6 marks] e) Determine a value of i, for which the LHS and RHS of the equation of equivalence vary by no more than $1.00. 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] f) Thus determine the effective interest rate, j1z, that this scholarship returns [2 marks]