Problem $2.($Spring $2021$ #$4,$ edited$)$ You sell a software product that you developed

and receive three payment options:

Option I is to receive a lump sum payment of $$1,000,000$ now.

Option II is to receive a lump sum payment of $$1,200,000$ three years from now.

Option III is to receive payment at a rate of $70000t^2$ dollars$/$year for the next three

years, where $t$ is time from the present in years. The $1$st payment starts one year after.

Assume you can get $5\%$ interest, compounded continuously. Which option leaves you with

the most money after three years?