Caroline is a socialite who was endowed with a large amount of old money. Over time Caroline, through her social activities, has spent large amounts of this money, but has realised the need to plan for retirement. After talking to friends in the investment industry she invested $200,000 of her remaining money into a fund.

If Caroline wanted to have $2,000,000 in her account by retirement in 20 years what rate of return on her investment would she need to achieve?

(2 marks)

Caroline is surprised by the growth of the capital in the fund. At the end of three years her money had grown to $350,000.

What rate of return is achieved on her money over the first three years?

(2 marks)

Based on her goal of $2,000,000 what rate of return would she now have to achieve to reach this goal?

(2 marks)

Caroline is unconvinced that the fund will continue to grow at this rate, and is convinced that the fund may possibly depreciate in value. She now aims to protect this money by investing the $350,000 into a term deposit with additional monthly payments into the account, paid at the end of each month. The term deposit pays 8% p.a. with interest compounded quarterly.

How large are the monthly deposits such that the fund will grow to $2,000,000 in the remaining 17 years?

(4 marks)

An alternative investment opportunity has occurred for Caroline to invest her current amount of $350,000. The investment has an upfront fee of $1,000 with fixed weekly payments into the account of $400 which are paid at the beginning of the week. The account pays a slightly lower rate of return at 7.75% p.a. compounded weekly.

Given that Caroline still wants $2,000,000 for her retirement in 17 years, identify which of the investments, either the monthly or weekly term deposit that generates the $2,000,000 the quickest.

(4 marks)

Identify, through discussion, the difference between an annuity due, an ordinary annuity and a general annuity?

(3 marks)