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.