Two friends, Alysha and Nancy, are planning for their retirement. Both are $20$ years old and plan on retiring in $40$ years with $$1,000,000$ each. Nancy plans on making annual deposits beginning in one year $($total of $40$ deposits$)$ while Alysha plans on waiting and then depositing twice as much as Nancy deposits.

If both can earn $8\mathrm{.}80$ percent per year, how long can Alysha wait before she has to start making her deposits? $($Round answer to $2$ decimal places, e$.$g$.125.$ Do not round your intermediate calculations.$)$

Alysha can wait for

years