The $$41\mathrm{.}8$ million lottery payment that you just won actually pays $$2\mathrm{.}2$ million per year for $19$ years. If the discount rate is $12\mathrm{.}50\%$ and the first payment comes in $1$ year.

a$.$

What is the present value of the winnings? $($Do not round intermediate calculations. Enter your answer in millions rounded to $2$ decimal places.$)$

Present value $

million

b$.$

What is the present value of the winnings, if the first payment comes immediately? $($Do not round intermediate calculations. Enter your answer in millions rounded to $2$ decimal places.$)$

Present value $

million