Continuous Compounding Interest Calculator

Continuous Compounding Formula:

\[ FV = P \times e^{r \times t} \]

Future Value (FV):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Continuous Compounding?

Continuous compounding is the mathematical limit that compound interest can reach if it's calculated and reinvested into an account's balance over an infinite number of periods. While not actually possible in practice, it's a useful concept in finance and mathematics.

2. How Does the Calculator Work?

The calculator uses the continuous compounding formula:

\[ FV = P \times e^{r \times t} \]

Where:

\( FV \) — Future Value
\( P \) — Principal amount (initial investment)
\( e \) — Euler's number (~2.71828)
\( r \) — Annual interest rate (in decimal)
\( t \) — Time in years

Explanation: The formula calculates how much an investment grows when interest is compounded continuously, rather than at discrete intervals (like annually or monthly).

3. Importance of Continuous Compounding

Details: Continuous compounding is important in theoretical finance and is used in various financial models, including option pricing models like Black-Scholes. It represents the upper limit of how much compound interest can grow.

4. Using the Calculator

Tips: Enter the principal amount in USD, annual interest rate as a percentage (e.g., 5 for 5%), and time period in years. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How is continuous compounding different from regular compounding?
A: Regular compounding calculates interest at specific intervals (e.g., annually, quarterly), while continuous compounding assumes an infinite number of compounding periods.

Q2: Is continuous compounding used in real banking?
A: While banks don't actually compound continuously, some financial products use formulas based on continuous compounding for theoretical calculations.

Q3: What is e in the formula?
A: e is Euler's number (~2.71828), a fundamental mathematical constant that appears in growth and decay problems.

Q4: How accurate is this for real investments?
A: For practical purposes, daily compounding gives nearly identical results to continuous compounding.

Q5: Can I use this for debt calculations?
A: Yes, the same formula applies to continuously compounded debt, though most loans use discrete compounding periods.