FV of Lump Sum
Calculates the future value when interest compounds continuously.
When to use: Use for theoretical maximum compounding, common in academic finance and derivative pricing.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| FV | Future Value | The value of the investment at a future date | $ |
| PV | Present Value | The current worth of a future sum | $ |
| k | Interest Rate | Nominal annual interest rate as a decimal | % |
| n | Number of Years | Investment time horizon in years | years |
Real-Life Examples
Example 1: Theoretical Maximum Growth
What is $10,000 worth in 20 years at 7% with continuous compounding?
Given
Step-by-Step
Continuous compounding yields $40,552.00 — slightly more than annual compounding ($38,696.84).
Example 2: Short-Term Deposit
$100,000 deposited at 3% continuously compounded for 2 years.
Given
Step-by-Step
The deposit grows to $106,183.65 with continuous compounding.
Frequently Asked Questions
Continuous compounding assumes interest is calculated and added to the principal an infinite number of times per year. It uses the mathematical constant e (approximately 2.71828) and represents the theoretical maximum growth rate for a given nominal interest rate.
While no bank compounds truly continuously, the concept is widely used in academic finance, derivative pricing (like the Black-Scholes model), and as a convenient mathematical approximation. Some high-frequency financial instruments approximate continuous compounding closely.
The difference depends on the interest rate and time period. For moderate rates (5-10%) over typical time horizons, continuous compounding yields roughly 0.5% to 2% more than annual compounding on the total return. The gap widens with higher rates and longer periods.