# Continuous Compound Interest Formula

## Formula

`Compound interest = PV x (ein - 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 (ein - 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 (ein - 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.

Continuous Compound Interest Formula July 7th, 2017

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