Can someone please help me understand how to solve a question like this?

A star player in the NBA is offered a 6-year contract by a team and two choices of compensation. In the first he is offered a lump sum of $40,000,000, paid at the beginning of his contract. In the second he is offered an initial payment of $6,000,000 and 6-year continuous income stream at the rate of $7,500,000 per year deposited into a savings account paying 8% annual interest, compounded continuously. Assuming that the player can also invest his money with the same interest of 8%, determine which plan is better for the player?





The formulas that I can use are as follows





Present Value = integral from T to 0 of ( I(t)*e^-rt) dt where T = time in years, I(t) is the income stream, r - interest rate, and t = current time





Future Value = integral of T to 0 of (S(t)*e^r(T-t))dt where S(t) is the income stream.





I have tried both but my answers are way off from what has been given to us (Plan 2 generates 41,739,057.02 dollars as payment) If someone can PLEASE help me understand this it will be much appreciated T.T|||Hints: First, note that you negate the integral to interchange the limits. Then, integrate the function w/respect to time. Finally, apply FTC (First Fundamental Theorem of Calculus).





Good luck!