Question1 [20 marks] You have the opportunity to join a syndicate which intends to search for the lost treasure of the Egyptian Pharaoh, Tutem KMoon. To join this syndicate you will need to have saved $50,000 in eighteen (18) months. You plan to do this by making regular monthly deposits of the same size into a savings account, starting in one month's time. The savings account pays interest j12 = 7.50% p.a. Illustrate this scenario as a fully labelled time line diagram. [2 marks] b) Determine the monthly deposit size required to reach your goal. [3 marks] c) Explain and perform a sanity check on your answer to (b) [1 + 1 = 2 marks] d) During the sixth month you lose your wallet. If you can't find it, you can't make your sixth deposit. If you can't make your sixth deposit [but can make deposits 7 to 18 of the size you found in part (b)], determine how much you will have accumulated in your savings account by the end of the 13th month. Determine how far short you would fall of your target. [6 marks] e) You find your wallet and don't miss the sixth deposit. Immediately after your gth deposit, the interest rate increases to j127.68 % p.a. Determine what deposit size will now be needed for deposits 9 to 18 in order to still meet your original target of $50000. Describe and perform a sanity check on your