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 5^th 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%?

(iii) 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 using a semi-annual rate of 5.0%?