Mr. Gates sold his successful IT business today in return for a fixed stream of payments to be received over a

period of 5 years. Each payment is $100,000. The first payment will be received 6 months after today and the

payments will continue semi- annually until the end of the 5th year. Mr Gates approaches his bank to borrow some

money which will be secured by the present value of the future income stream.

(i) What is the Present Value of the future income stream using a semi-annual compounding interest rate of 4.00%?

(2 marks)

(i) What is the Present Value of the future income stream using the same

information as for part (i) except that each payment is made at the start of each 6 month period? (2 marks)

(ii) Mr. Gates rejected an alternative proposal to receive a payment of $20,000 every 6 months with the same terms

as part (i) except that the payments would continue in perpetuity (forever). Assuming that there is no risk of failure

to make the future payments, what is the Present Value of the perpetuity usinq a semi-annual rate of 5.0%? (2

marks)