George Bogut just received a signing bonus of $$1,071,000.$ His plan is to invest this payment in a fund that will earn $8\%,$ compounded annually.

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$($a$)$

If Bogut plans to establish the AB Foundation once the fund grows to $$2,140,929,$ how many years until he can establish the foundation? $($Round factor values to $5$ decimal places, e$.$g$.1\mathrm{.}25124$ and final answer to $0$ decimal places, e$.$g$.25.)$

years