# ordinary annuity

## 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.

### Derivation

$F = \text{ Sum}$

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

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

## Types of Annuities

**Types of Simple Annuities**

In engineering economy, annuities are classified into four categories. These are: (1) ordinary annuity, (2) annuity due, (3) deferred annuity, and (4) perpetuity. These four are actually simple annuities described in the previous page.

- Read more about Types of Annuities
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