You win $$100,000,000$ in a lottery. The lottery commission offers you two options: $(1)$ You can take the lump sum $$59,506,497$ now. $(2)$ You can get $$1,505,143$ now and get periodic yearly payments that grow at $5\%$ per year for the next $29$ years. $($That is$,$ in one year you get $$1,505,143(1\mathrm{.}05),$ in two years you get $$1,505,143(1\mathrm{.}05)(1\mathrm{.}05),$ and so on for $29$ years.$)$ What is the implicit discount rate the lottery commission is using if you take the lump sum payout of $$59,506,497?$ You can solve this problem using the Goal Seek function or the Solver function in Excel.