The future value of a single-period investment can be expressed in a generalized form using the formula:

$$FV=C_{0}\times (1+r)^{t}$$

C_{0}— 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.