## 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.