Two friends, Alysha and Betty, are planning for their retirement. Both are $20$ years old and plan on retiring in $40$ years with $$1,000,000$

each. Betty 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 Betty deposits.

If both can earn $4\mathrm{.}20$ 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