How many men paid for a total amount of $262,143.75 if the first person to arrive only paid 25 cents?

Problem
In a fund raising show, a group of philanthropists agreed that the first one to arrive would pay 25¢ to enter, and each later would pay twice as much as the preceding person. The total amount collected from all of them was $262,143.75. How many of them paid?

Derivation of Formula for the Future Amount of Ordinary Annuity

The sum of ordinary annuity is given by
 

F=A[(1+i)n1]i

 

To learn more about annuity, see this page: ordinary annuity, deferred annuity, annuity due, and perpetuity.
 

Derivation

Figure for Derivation of Sum of Ordinary Annuity

 

F= Sum

F=A+F1+F2+F3++Fn1+Fn

F=A+A(1+i)+A(1+i)2+A(1+i)3++A(1+i)n1+A(1+i)n