The future value of a single-period investment can be expressed in a generalized form using the formula:
$$FV=C_{0}\times (1+r)^{t}$$
C0— initial investment, present value;
r— interest rate;
t— number of periods.
If interest is compounded n times a year, the future value can be calculated using the following formula:
$$FV=C_{0}\times \left (1+\frac{r}{n}\right )^{n\times t}$$
r— annual interest rate;
n— number of compounding periods per year.
Interest can be compounded annually, semi-annually, quarterly, monthly, daily, hourly, every minute, or even more frequently. If n → ∞ in the formula above, the future value can be calculated using the formula:
$$FV=C_{0}\times e^{r\times t}$$
r— annual interest rate;
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.