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 months time. The savings account pays interest j₁₂ = 7.50% p.a.

• 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 cant find it, you cant make your sixth deposit. If you cant 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 18^th month. Determine how far short you would fall of your target.

[6 marks]

• e) You find your wallet and dont miss the sixth deposit. Immediately after your 8^th deposit, the interest rate increases to j₁₂=7.68 % 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 answer.