The present value of an annuity. An **annuity** is a series of periodic constant cash flows, either received or paid out, lasting for a fixed period.
**Ordinary annuity** payments occur at the end of each payment period. The present value of an ordinary annuity is found using the following formula:

$$PV_{Ordinary\; Annuity}=C \times \left[\frac{1-(1+r)^{-t}}{r}\right]$$

C— periodic payment amount;

r— periodic discount rate;

t— number of periods.

**Annuity due** payments occur at the beginning of each payment period. Examples include rent or lease payments. The present value of an annuity due is calculated using the following formula:

$$PV_{Annuity\; Due}=C \times \left[\frac{1-(1+r)^{-t}}{r}\right]\times(1+r)$$

C— periodic payment amount;

r— periodic discount rate;

t— number of periods.

**Growing annuity** is a series of periodic cash flows that lasts for a fixed period and increases at a constant rate each year.
The present value of a growing annuity can be calculated using the formula:

$$PV=\frac{C_{0}}{r-g} \times \left[1-\left(\frac{1+g}{1+r}\right)^{t}\right]$$

C_{0}— initial payment;

g— growth rate;

r— discount rate;

t— number of periods.

**Euler's number or Euler's constant e** is expressed as a limit:

$$e=\lim_{n\rightarrow \infty }\left ( 1+\frac{1}{n} \right )^{n}=2,71828\; 18284\; 59045\; 23536... $$

**Leonhard Euler** (April 15, 1707, Basel – September 18, 1783, St. Petersburg) was a Swiss mathematician and physicist who spent much of his life in Russia, in St. Petersburg, and in Germany, in Berlin. Euler proved that e is an irrational number and computed the first 18 digits of the constant in 1748.