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

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

$F = \dfrac{A[ \, (1 + i)^n - 1 \, ]}{i}$


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


Figure for Derivation of Sum of Ordinary Annuity


$F = \text{ Sum}$

$F = A + F_1 + F_2 + F_3 + \cdots + F_{n-1} + F_n$

$F = A + A(1 + i) + A(1 + i)^2 + A(1 + i)^3 + \cdots + A(1 + i)^{n-1} + A(1 + i)^n$