The future value of an annuity. **Annuity** is a series of periodic constant cash flows received or paid out, lasting until a fixed term.
**Ordinary annuity** payments occur at the end of each payment period. The future value of an ordinary annuity is calculated using the following formula:

$$FV_{Ordinary\; Annuity}=C \times \frac{(1+r)^{t}-1}{r}$$

C— periodic payment amount;

r— period interest rate;

t— number of periods.

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

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

C— periodic payment amount;

r— period interest rate;

t— number of periods.

**Formula for the future value of a growing annuity** can be used when payments grow at a constant growth rate. The formula is:

$$FV_{ga}=C \times \left[\frac{(1+r)^{t}-(1+g)^{t}}{r-g}\right]$$

**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 calculated the first 18 decimal places of the constant in 1748.