Calculated from the sample figures using the displayed formula.
What is the continuous compound interest formula?
A = PeʳᵗContinuous compounding is the limiting case in which interest is compounded at every instant.
What do the inputs mean?
- Starting principal
- The value entered for starting principal. Keep its period and units consistent with the other inputs.
- Annual rate (%)
- The value entered for annual rate (%). Keep its period and units consistent with the other inputs.
- Years
- The value entered for years. Keep its period and units consistent with the other inputs.
How to calculate it step by step
- Define the decision.
Write down what the result will help you compare or decide. - Collect matching inputs.
Use figures from the same period and apply the definitions shown on this page. - Apply the formula.
A = Peʳᵗ. - Check the units.
Confirm whether the result is a currency amount, percentage, number of periods or ratio. - Test a second case.
Change one assumption at a time to see what drives the result.
Worked example
Using the sample figures in the calculator, the result is $18,221.19. Change one figure at a time and recalculate to see which assumption has the greatest effect. A spreadsheet should return the same result when it uses the same formula, units and timing.
When should you use continuous compound interest formula?
Use it in mathematical finance models that explicitly specify a continuously compounded rate.
Limitations and common mistakes
Do not substitute continuous compounding when a quoted product compounds monthly, daily or annually.
Do not mix annual figures with monthly figures, ending balances with averages, or percentages with whole numbers. Record the definition used so another person can reproduce the result.
Frequently asked questions
What is continuous compound interest formula?
Continuous compounding is the limiting case in which interest is compounded at every instant.
How should I use continuous compound interest formula?
Use the formula only after matching every input to the same period, unit and definition. Then compare the result with a worked example and the decision you are trying to make.
What is the most common mistake with continuous compound interest formula?
Do not substitute continuous compounding when a quoted product compounds monthly, daily or annually.
Can I calculate continuous compound interest formula in a spreadsheet?
Yes. Reproduce the displayed equation with separate cells for each input, keep percentages as decimals, and test the spreadsheet against the worked example before replacing the sample figures.
Sources and methodology
This page uses the Investor.gov Compound Interest Calculator for the underlying financial or reporting context. Spreadsheet-related behavior is checked against Microsoft’s financial-function documentation. Examples are illustrative and use the formula displayed on the page.