You are saving to buy a $$178,000$ house. There are two competing banks in your area, both offering certificates of deposit yielding $6\mathrm{.}3$ percent.

a$.$ How long will it take your initial $$95,000$ investment to reach the desired level at First Bank, which pays simple interest?

Note: 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 $$95,000$ investment to reach the desired level at Second Bank, which compounds interest monthly?

Note: 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