5. Little Jimmy, who is just 14 years old, has won a lottery. The lottery does not pay out any money until a person is at least age 21. Jimmy hires a consultant and this consultant suggests that Jimmy invest the money and then begin receiving monthly payments of $1800 once he reaches age 21. The consultant also suggests that Jimmy should protect himself from inflation by having his payments increase by 2.1% each year. The 12 monthly payments in year 1 will be $1800 (age 21 to age 21, 11 months), the 12 monthly payments for year 2 will be 1800(1.021) (age 22 to age 22, 11 months), the 12 monthly payments for year 3 will be 1800(1.021)2 (age 23 to age 23, 11 months) and so on. (This is a situation where the payments are monthly, but the percentage increase is annually). Jimmy has won enough money for this payment scheme to last for a total of 30 years. If Jimmy can earn i = 5% on his winnings and if the consultant charges 1.5% of the winnings as a fee (payable up front when Jimmy is 14), how much did Jimmy win in the lottery? (6 marks)