## Formula

Compound interest = PV x (e^{in}- 1)

**Variables used in the formula**

PV = Present value

i = Discount rate per period

n = Number of periods

e = Base of the natural logarithm (LN) ≈ 2.71828

## Use

The continuous compound interest formula shows the interest accumulated at the end of a time (n) on an amount (PV) deposited today and compounded continuously at an interest rate (i).

## Example 1 using the Continuous Compound Interest Formula

If an amount of 7,000 is deposited at time zero (today) and is compounded continuously for a period of 4 years at an an interest rate of 5%, then the compound interest at the end of year 4 is given by the continuous interest formula as follows:

Compound interest = PV x (e^{in}- 1) Compound interest = 7000 x (e^{(5% x 4)}- 1) Compound interest = 1,549.82

## Example 2 using the Continuous Compound Interest Formula

If an amount of 4,000 is deposited at time zero (today) and is compounded continuously for a period of 24 months years at an an interest rate of 6%, then the compound interest at the end of month 24 is given by the continuous interest formula as follows:

Compound interest = PV x (e^{in}- 1) Compound interest = 4000 x (e^{(6%/12 x 24)}- 1) Compound interest = 509.99

The continuous compound interest formula is one of many formulas used in time value of money calculations, discover another at the links below.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years in all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.