## How the Continuous Compound Interest Calculator can help you

Continuous Compound Interest Calculator help you to see how fast the continuous compound interest formula converges.

## How to use the Continuous Compound Interest Calculator

1. Enter the “Starting Principal”;

2. Enter the “Interest Rate”;

3. Enter the “Years”;

4. Click on “Calculate” button to get the result.

## Continuous Compound Interest Calculator Meaning

**Continuously**, meaning that your balance grows by a small amount every instant.

## Continuous Compound Interest Calculator Formula

We’ll start out with interest compounded n times per year to get the Continuous Compound Interest Calculator formula (Where P is the starting principal and FV is the future value after Y years.):

FVn = P(1 + r/n)

^{Yn}

We take the limit as the time slices get tiny to get to the continuous case:

FV = limit P(1 + r/n)

^{Yn}

**Defining m = n/r** to simplify the right side, So the formula changes to

FV = limit P(1 + 1/m)

^{Ym}= P [limit (1 + 1/m)^{m}]^{Yr}

The limit in the square brackets converges to the number e = 2.71828…..So the formula becomes:

FV = Pe

^{Yr}

## In Calculus

Replace “FV” notation, and write f(t) for the balance at time t (with t measured in years). So the formula becomes:

f(t) = Pe

^{tr}

After we take the derivative, the formula becomes:

## Definition Of Continuous Compound Interest

At any instant the balance is changing at a rate that equals r times the current balance.