The Heavens Gate Group have $$33$ million in cash. In order to reach the comet that will take them to a new world they need the $$33$ million to grow to $$90$ million. How many years will it take before the group can leave if they earn $11\mathrm{.}4\%$ per annum on their stash of cash? Assume annual compounding. $($Enter your answer in years to $2$ decimal places, e$.$g$.,12\mathrm{.}34)$

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