Please explain which Excel formula you used, the reason behind your choice, and include Excel tables in the solution.

An American baseball outfielder$$s $$325$ million contract with a baseball firm has $13-$year payout schedule and it looks like the following:

$2015$:$ $6\mathrm{.}5$ million

$2016$:$ $9$ million

$2017$:$ $14\mathrm{.}5$ million

$2018$:$ $25$ million

$2019$:$ $26$ million

$2020$:$ $26$million

$2021$:$ $29$ million

$2022$:$ $32$ million

$2023$$ $32$ million

$2024$:$ $32$ million

$2025$ $ $32$ million

$2026$:$ $29$million

$2027$:$ $25$ million plus $$10$ million buyout option

Note that the deal allow him to opt out after the end of $2020$ World Series, but if he does, he leaves a substantial sum of money on the table by opting for free agency. In years $2015-20$ he will earn $$107$ million of the $$325$ million deal, but in years $2021-26$ where he would leave the team, the salaries total $$218$ million would be foregone, or more than twice the sum of the early years in the contract.

$($a$)$ With the salary paid at the beginning of each season, what is the worth of his contract at the interest rate of $6\%?$

$($b$)$ Suppose he got another contract at the end of the $2020$ season being a free agent valued at $$210$ million to be paid over $7$ seasons $($$$30$ million paid at the beginning of each season$).$

Is it worth being a free agent to take this offer at $6\%$ interest?