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.
Finding Future Value for multi-period investment
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.
Finding Future Value with Continuous Compounding
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;
Additional Reading
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.
See Also:
Future Value FAQ
What is future value?
It is the value an investment grows to in the future.
How do you calculate it?
Use the present amount, interest rate, and number of periods.
