A businessman wants to donate the funds to establish a new academic support program for student athletes. He is prepared to donate $10 million today (Feb. 16, 2012), one year hence (Feb. 16, 2013), and two years hence (Feb. 16, 2014) to establish an annuity to pay for the operations of the program. The annuity will pay a constant annual amount X on Feb. 16 of each year starting in 2015.
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?)