Congratulations! You Just won the $$100$M Jackpot lottery. You have two options to collect your winnings:

Option $1$: An annuity paying $$2\mathrm{.}5$M per year for $40$ years with the first payment occurring in $1$ year.

Option $2$: A lump sum $($paid $100\%$ in full today$)$ of $$58$M$.$

What is the implied interest rate of the annuity?

$($Hint: What interest rate makes the $40-$year annuity equal to the lump sum today?$)$