Continuous Compound Interest Calculator

Continuous Compound Interest Calculator
Starting Principal:($)
Interest Rate: (%)
Years:
Future Value
Periodic compounding: P(1 + r/n)Yn for n equal to...
1 ($)
($)
12 ($)
365 ($)
365 x 24 ($)
Continuous compounding:
PeYr ($)

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 = PeYr

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) = Petr

After we take the derivative, the formula becomes:
Continuous Compound Interest Calculator

Definition Of Continuous Compound Interest

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