You are saving to buy a $$177,000$ house. There are two competing banks in your area, both offering certificates of deposit yielding $6\mathrm{.}2$ percent.

a$.$ How long will it take your initial $$94,000$ investment to reach the desired level at First Bank, which pays simple interest? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ How long will it take your initial $$94,000$ investment to reach the desired level at Second Bank, which compounds interest monthly? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

a$.$ Years to wait at First Bank

b$.$ Years to wait at Second Bank