1. Congratulations! You have just won your states local lottery. The lottery will pay out $1,000,000 at the end of each year for the next 25 years. While the Lottery Commission refers to this as a $25,000,000 jackpot, if you choose the cash option they will give you much less than that; you can receive a lump sum payment today equal to the present value of the ordinary annuity instead of the 25 annual payments. If the discount rate that the Lottery Commission uses to determine the lump sum payoff is 7.5%, what is your payoff if you select the cash option?

1. $9,147,286.58
2. $11,146,945.86
3. $16,481,514.59
4. $19,072715.05

Would you please use the BA II Plus calculator (TVM --> N, PMT, I/Y, FV, and PV)? The formula from the previous examples gives me a different answer. I got $11,146,933.33 when I use the following formula Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate. Could you explain why?