Finance & Investment · Interest
Continuous Compound Interest Calculator
Work out continuous compound interest — A = P·e^(rt) — and solve for whichever one you don't know: the final amount, how long it takes to reach a target, the rate you need, or the starting amount needed today. Compare with annual, monthly and daily compounding and see the effective annual rate and the doubling time.
Your inputs
₹ 1 lakh
Your result Live
Final Amount
₹2,22,554
₹1,00,000 at 8% compounded continuously for 10 years
- Starting Amount
- ₹1,00,000
- Total Interest Earned
- ₹1,22,554
- Rate
- 8.000%
- Time
- 10 years
- Effective Annual Rate
- 8.329%
- Time to Double
- 8.66 years
- Growth Multiple
- 2.226×
- Same Rate, Compounded Annually
- ₹2,15,892 (-₹6,662)
- Same Rate, Compounded Monthly
- ₹2,21,964 (-₹590)
- Same Rate, Compounded Daily
- ₹2,22,535 (-₹20)
- Principal · 45%₹1,00,000
- Interest · 55%₹1,22,554
Year-by-year growth
10 rowsAn estimate from the assumptions you entered, not a guaranteed outcome.
How this is calculated
A = P × e^(r × t) · t = ln(A ÷ P) ÷ r · r = ln(A ÷ P) ÷ t · P = A × e^(−r × t)
- A
- Final amount
- P
- Principal (starting amount)
- r
- Annual interest rate (decimal)
- t
- Time in years
- e
- Euler's number, about 2.71828
Continuous compounding is the limit of compounding more and more often: every instant, interest is added and starts earning interest. The balance then follows A = P·e^(rt). It is the ceiling for any compounding frequency — 8 % compounded continuously is an effective 8.329 % a year, against 8.243 % quarterly and 8 % annually — and it is the standard in finance theory and option pricing. Real bank accounts compound at most daily, which is within a rounding error of continuous. Solving the formula backwards gives the time or rate a target needs, using natural logarithms.
Assumptions & sources
- The rate stays the same for the whole period and nothing is added or withdrawn.
- Interest is compounded continuously; no real account does this exactly, but daily compounding is almost identical.
- Tax on the interest is not deducted.
- Time to reach a target is limited to 100 years.
- 1Investments (Bodie, Kane & Marcus), chapters on returns, compounding and the time value of money — McGraw-Hill
- 2CFA Program Curriculum — Quantitative Methods: The Time Value of Money — CFA Institute
Calculator ID FIN-INT-CCI-001 · version 1.0.0
Common questions
What is the continuous compound interest formula?
A = P × e^(r × t), where P is the principal, r the annual rate as a decimal (8 % = 0.08), t the time in years and e ≈ 2.71828. For ₹1,00,000 at 8 % for 10 years: 1,00,000 × e^0.8 = ₹2,22,554.
How much more does continuous compounding earn than daily or monthly?
Very little. At 8 % for 10 years on ₹1,00,000, annual compounding gives ₹2,15,892, monthly ₹2,21,964, daily ₹2,22,535 and continuous ₹2,22,554. Most of the gain comes from compounding more often than once a year.
How do I find how long it takes to reach a target?
Choose Time needed. The calculator uses t = ln(A ÷ P) ÷ r. For example, doubling money at 8 % takes ln 2 ÷ 0.08 ≈ 8.66 years.
Why use continuous compounding if banks don't?
It gives clean formulas, and it is the upper limit that any compounding frequency approaches. Finance theory (option pricing, discounting) uses it, and it's a good quick estimate for daily-compounded accounts.