Suppose you have won a lottery that promises to pay you a lump sum of $500,000 today or an annuity with payments of $5,000 at the end of every month for 20 years. If you believe you can earn 6 percent per annum on your investments, should you take the lump sum (and invest the proceeds yourself), or the annuity? Why? For full or partial credit, please be sure to show your work and label your inputs.