# Derivation of Formula for the Future Amount of Ordinary Annuity

The sum of ordinary annuity is given by

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

### Derivation

$F = \text{ Sum}$

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

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