Question 2: Using Indices and Compounding Interest A 24-year-old economics graduate has just secured their first full time position and is aiming to save a reasonable deposit to buy a small apartment. As such, the graduate must consider a savings strategy. The graduate is aiming to have $100 000 saved over 5 years. Task - Part 1 Using information given below, determine the average rate of return required for the employee to reach this savings target: The graduate's initial annual salary (at age 24, after tax) is $51 000, of which they can contribute between 9.5% and 12% towards superannuateon After making their superannuateon contribution, the graduate's living expenses must be accounted for. During the first year, these amount to $26 000. In subsequent years, expenses are assumed to increase by 3.25% each year. Anything left remaining after living expenses represents potential savings to be put aside for the house deposit. In this instance, the account that the graduate is depositing these savings into is a non-interest bearing account (with a commencing balance of zero). The graduate's salary over the next 5 years is predicted to change as follows: At the end of Year 2, a pay increase of 1.5% At the end of Year 3, a pay increase of 2% At the end of Year 4, a final pay increase of 0.75% Steps to answer Part 1 a) Determine the graduate's salary for each of the five years. b) Determine the graduate's superannuateon contributions for each of the five years. For this section you must pick your own value between 9.5% and 12% and use this value for all five years. c) Determine the graduate's living expenses for each of the five years. Then, from there, determine the amount remaining that could be put towards a housing deposit per year over 5 years. d) If the graduate does not reach their savings target at the end of 5 years, determine the time required for the graduate to reach their savings goal if they were to place all of the savings accumulated up to that point (i.e. by end of Year 5) into a savings account which accumulates interest compounded annually at 4.65%. Task - Part 2 At the age of 29, due to circumstances beyond their control, the graduate has to withdraw $25 000 back out from the account into which they have been depositing their savings. The graduate is then faced with a choice: . Put the remaining balance into an interest-bearing account with a guaranteed return of 6.99% per annum, compounding monthly. Put the remaining balance into an interest-bearing account with a guaranteed return of 2.49% per annum, compounding quarterly. Step to answer Part 2 For both interest-bearing account options, determine how long it would take the graduate's account balance to reach $100 000. Express your answers in months and years (to two decimal places)