The XYZ Company is offering the public a retirement scheme that pays $30,000 a year for a maximum period of 25 years, with the first payment beginning in 21 years' time. It is offering the following payment schemes:

Option 1

Pay $10,000 a year over a period of 10 years, with the first payment to be made in one year's time.

Option 2

In one year's time pay $7,000 with the amount growing by 5% each year for a total period of payments of 20 years.

Option 3

Make a total of 10 payments of $20,000. The first payment begins in two years' time with payment made every two years.

(a)Calculate the present value of each option using a discount rate of 8%. (15 marks)

(b)Discuss which option should be chosen? (7 marks)

(c) Suppose the retirement scheme makes the payments for as long as the retiree lives,

instead of a maximum of 25 years. Briefly discuss XYZ Company's considerations regarding extending the payments for a lifetime to the following applicants:

1. Mr Tan, aged 50
2. Ms Lim, aged 40 (6 marks)