1. Two annuities are available for purchase that your client has identified. The first annuity pays $2,800 each month over a 5 year period at a nominal rate of 9% p.a. The second annuity pays $18,000 each six-month period, again over 5 years, at a nominal rate of 10% p.a., but has an annual fee of $1,000, paid at the beginning of each year. Identify which of the two annuities would be a better option for your client.

2. Your clients parents have a business with a loan of $5,000,000 repayable at the end of each year at a nominal rate of 9.5% p.a., compounded monthly. The business now wishes to contemplate converting to payments on a quarterly basis. The loan is for 5 years. Your client would like to know:

   (a) What is the current annual payment on the loan? (b) What will be the payment if the business switches to payments at the beginning of each quarter?

3. Your client would like to have $15,000 in 15 years time for a luxury holiday with her husband to celebrate their silver anniversary (25th wedding anniversary). If she has an opportunity cost of 10% per annum, compounded semi-annually, how much does she need to invest each year to have $15,000 accumulated in 15 years?