Gabrielle just won $$2\mathrm{.}5$ million in the state lottery. She is given the option of receiving a total of $$1\mathrm{.}3$ million now, or she can elect to be paid $$100,000$ at the end of each of the next $25$ years. If Gabrielle can earn $5\%$ annually on her investments, from a strict economic point view, which option should she take?

Can you please show step$-$by$-$step detail on how to solve this problem?