Several years ago, Shin Lim, a magician, won Americas Got Talent contest. His prize of $1,000,000 could be paid out as an ordinary annuity of $25,000 per year over 40 years. Alternatively, Shin could take a one-time cash payout of $350,000. If Shin could earn 3% interest per year on his money and there are no tax differences to selecting either option, which option should he have selected and why?

Please show work!