Lottery Winnings

The $$78\mathrm{.}3$ million lottery payment that you just won actually pays $$2\mathrm{.}9$ million per year for $27$ years. If the discount rate is $7\mathrm{.}50\%$ 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

$$$35\mathrm{.}562$ million