Problem:
Paul wants to donate the funds to establish a new academic support program for student athletes in the Department of Athletics. Specifically, he is prepared to donate $10 million today (Feb. 12, 2015), $10 million one year hence (Feb. 12, 2016), and $10 million two years hence (Feb. 12, 2017) to establish an annuity to pay for the operations of the program. The annuity will pay a constant annual amount X on Feb. 12 of each year starting in 2018.
If the annual interest rate (compounded annually) is r, what is the maximum amount the annuity can pay? (That is, what is the maximum value X can be?)
Explain comprehensively and show all workings and techniques.