You have won a lottery and can choose to receive the payment under one of the following two arrangements:

1. (1) $250,000 every six months forever, or

2. (2) fixed payments of $X every six months for 15 years.

Suppose the relevant half-yearly rate is 5% and the payments under both arrangements will start immediately.

i) How much is the lottery worth today under Arrangement (1)? (4 marks)

ii) What is the amount of $X in Arrangement (2) so that it has the same value as Arrangement (1)? (4 marks)