Baseball pitcher Chris Sale signed a contract in $2019$ to play for the Boston Red Sox for $5$ years at an annual salary of$$ $$29$ million per year beginning in $2020.$ But he would not actually receive the full amount of his annual salary each year. The Red Sox would not begin to pay$$ $$50$ million of his salary until the year$2035,$ when he would receive$$ $$10$ million per year through $2039.$

Part $2$

An article on espn.com discussing$$ Sale's contract noted that$$ "the five$-$year deal is worth$$ $$145$ million." The author of the article arrived at this total$$ "worth" of$$ Sale's contract by

adding up his $$29$ million yearly salary over $5$ years

$.$

Do you agree with the author that the contract was actually worth$$ $$145$ million to$$ Sale?

The author is

incorrect

$,$

the total worth of$$ Sale's contract will be

less than

$$$$145$ million once you consider the present value of all future payments.

Part $3$

Assume for simplicity that Sale receives a salary of$$ $$20$ million per year for the next $3$ years, with each payment coming at the end of each calendar year. This means he receives his first payment at the end of this$$ year, his second payment at the end of next$$ year, and his third payment at the end of the following year.

At the beginning of this$$ year, what is the present value of the salaries he will receive for these $3$ years if the interest rate is

$66\%?$

The present value of these payments would equal

$$$$23\mathrm{.}6723\mathrm{.}67$

million. $($Round your answer to $2$ decimal$$ places$)$