Continuous Compounding Calculator

Enter starting amount, annual interest rate, years to find future value. FV = Pe^(rt).

INPUT & RESULT

How the result changes

Years (years)Current: 10 → 16.5K currency units

Only years changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.

About this calculation

Continuous Compounding: find future value from starting amount, annual interest rate, years. Compound growth adds earned interest to the balance so future interest can accrue on it.

Formula

FV = Pe^(rt)

Worked example

With Starting amount: 10000 currency units, Annual interest rate: 5 %, Years: 10 years, future value is 16,487.21 currency units.

Calculation method

The rule is FV = Pe^(rt).

For this continuous compounding example, changing starting amount from 10000 currency units to 10001 currency units while keeping the other inputs fixed changes future value from 16,487.21 currency units to 16,488.86 currency units.

Reading future value

Future value projects an end balance; present value discounts a future sum back to the starting amount. Continuous compounding is a limiting mathematical case. In the worked values on this page, starting amount 10000 currency units, annual interest rate 5 %, years 10 years produce future value 16,487.21 currency units.

Practical use

Use the result to compare hypothetical rates, periods, and compounding conventions. The specific task here is to find future value from starting amount, annual interest rate, years.

Limits and common mistakes

A fixed rate and no extra cash flows are assumed. Fees, taxes, inflation, and actual investment variability are outside the formula. Verify starting amount in currency units before interpreting future value; a value measured on another basis would answer a different question.

Read the example and units

The worked values on this page use starting amount 10000 currency units, annual interest rate 5 %, and years 10 years. With those exact entries, the calculator reports future value 16,487.21 currency units. The same example also reports interest earned 6,487.21 currency units; those figures describe different aspects of this one set of inputs rather than extra values to add to the primary answer. Keep all money amounts in one currency and check which amount is the base of a percentage. The displayed rule uses only the rate, amount, term, or count you supply; it does not import a market price, account balance, receipt rule, or contract term.

Compare one changed input

For a second scenario, change only starting amount 10000 currency units to starting amount 11000 currency units and leave the other example entries alone. The result for future value changes from 16,487.21 currency units to 18,135.93 currency units. Comparing one changed input at a time shows exactly which assumption drove the difference in this calculation. This comparison isolates the arithmetic effect of one assumption. Actual fees, contract terms, taxes, behavior, or market outcomes may change a real result, so compare several plausible inputs rather than relying on one precise-looking number.

How to interpret this kind of result

Separate the starting principal from the return it earns. Simple interest applies the rate to the original amount each year; periodic or continuous compounding adds growth on top of earlier growth. Effective annual rate puts a nominal rate with periodic compounding on a one-year basis, which helps compare two rate conventions. Use the method named on this page, not a different compounding assumption. For this continuous compounding calculation, starting amount in currency units, annual interest rate in %, and years in years determine future value; the displayed future value 16,487.21 currency units belongs to that exact combination rather than to a different rate, term, or measurement basis.

Scope and practical checks

The annual rate is an input assumption, not an assured investment return. Timing of deposits, fees, taxes, inflation, and changing rates are outside these single-balance formulas unless shown explicitly. A comparison between scenarios should keep the starting amount and period consistent. For a savings product, verify how its provider credits interest before treating a projection as an account balance. This continuous-compounding model is the limiting case of ever more frequent compounding, not a bank promise of continuously credited interest. Check the starting amount in currency units, annual interest rate in %, and years in years entries against the quantities in your own situation before using future value; this page cannot infer a field or condition that you did not enter.

Common questions

What does this continuous compounding result include?

The future value comes from starting amount in currency units, annual interest rate in %, and years in years using the displayed rule FV = Pe^(rt). It does not automatically include a condition absent from the listed inputs. Check the applicable account, transaction, or contract terms before using it for a financial decision.