Investment Mathematics

15.8. Bob takes a long position in one contract of S&P 500 futures. Each contract is for the delivery of 250 units of the index at a price of 1800 per unit. The initial margin is 10% of the notional value and the maintenance margin is 80% of the initial margin. Interest on the margin account is paid at an annual continuously compounded rate of 5%. The first mark-to- market occurs one week (7 days) after the sale of the contract. Determine the lowest value of the futures contract not requiring a margin call