Why use continuous compounding at all?

Because e to the rt differentiates cleanly, which makes continuous-time finance workable. The extra return over daily compounding is negligible and is not the reason.

What is the rule of 72 doing here?

Under continuous compounding the exact doubling time is the natural log of two divided by the rate, about 69.3 over the rate as a percentage. The rule of 72 is a friendlier approximation of it.

Finance & Loansinterest

Continuous Compounding Calculator

Continuous compounding, and the surprisingly small amount it adds over compounding once a year. It is the mathematical ceiling on frequency, not a different kind of growth.

Also called: e^rt calculator, exponential growth money.

Value with continuous compounding

₹1,49,182

₹1,49,182 after 5 years. Compounding annually would give ₹1,46,933, so infinite compounding is worth only ₹2,250 more, which is the point of the exercise.

With annual compounding

₹1,46,933

With daily compounding

₹1,49,176

Continuous over annual

₹2,250

Effective annual rate

8.33%

Years to double

8.66

How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for India change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

Compounding more often earns more, but the gain converges: as the number of periods goes to infinity the factor approaches e to the power of the rate. At eight percent, annual compounding gives 8%, daily gives 8.33%, and continuous gives 8.33% as well to two places. The reason continuous compounding matters is not the extra money, it is that the exponential form makes the mathematics of options pricing and decay tractable.

value = principal * e ^ (rate * years)

P: Principal (currency)
r: Annual rate (decimal)
t: Years (years)

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

five years at eight percent

Principal: ₹1,00,000
Annual rate: 8%
Years: 5

Value with continuous compounding₹1,49,182

100000 * e^0.4, computed independently

Open this example

a zero rate never grows

Principal: ₹1,00,000
Annual rate: 0%
Years: 5

Value with continuous compounding₹1,00,000

boundary

Open this example

doubling time is ln 2 over the rate

Principal: ₹1,00,000
Annual rate: 10%
Years: 1

Value with continuous compounding₹1,10,517

degenerate case: the exact figure the rule of 72 approximates

Open this example

Method and limits

What it assumes

A constant rate.

What it deliberately does not model

No deposit product actually compounds continuously. It is a modelling convenience.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Why use continuous compounding at all?: Because e to the rt differentiates cleanly, which makes continuous-time finance workable. The extra return over daily compounding is negligible and is not the reason.
What is the rule of 72 doing here?: Under continuous compounding the exact doubling time is the natural log of two divided by the rate, about 69.3 over the rate as a percentage. The rule of 72 is a friendlier approximation of it.