#### Definition:

Continuous compounding is the procedure of obtaining interest on top of interest in a monthly, quarterly and semiannual basis. It is utilized to discover the future value of a present sum when investment is exacerbated persistently.

#### Formula:

FV = PV x e^{rt}
###### Where,

FV = Future value
PV = Present value
r = Interest rate
t = number of years
#### Example :

An amount of $5000.00 is deposited in a bank paying an annual interest rate of 5%, compounded continuously. Find the future value after 3 years.

##### Given,

PV = 5000
r = 5% = 0.05
t = 3

##### To Find,

Future value

##### Solution:

Substitute the given values in the formula,
FV = PV x e^{rt}
= 5000 x e^{0.05 x 3}
= 5000 x e^{0.15}
= 5000 x 1.161834
= 5809.17