## Continuously Compounding Periods

If compounding periods are continuous, it means that the time between them is considered to be
infinitesimally small, hence they are continuously compounding.

In this case, to calculate future and present values, use the following:

*f = p e*^{rn}

or,

*p = f e*^{-rn}

where:

f is future value

p is present value

e is the natural number, i.e. 2.7182...

r is periodic interest rate as a decimal value (not as a percentage)

n is the number periods

### Example

**Example:** *You have invested $2,000 dollars in a venture which offers an annual continuously
compounded return of 5%. How much will the investment be worth in 6 months?*

In RPN mode, key in:

**2000
[ENTER]**
**0.05** *(annual rate as fraction)*
**[ENTER]
0.5** *(6 months - half a period)*
**[×]
[e^x]
[×]**
Displays: 2050.63

See also: Compound Interest