You win the $$2$ million Georgia lottery. They promise you a payout of $$100,000$ a year for $20$

years. Knowing some finance you ask them for a lump sum payment today of $$1\mathrm{.}5$ million

instead of the $20$ yearly installments. You immediately take $$100,000$ out of the lump sum of

$$1\mathrm{.}5$ million and invest the rest for $19$ years at a rate of $5\%.$ If you withdraw $$100,000$ a year out

of this investment for the next $19$ years, how much will you have at the end of that period? Was

your idea a better way to take the payments? Explain your answer.