What Is Compound Interest? Formula, Examples, Frequency

Someone paying Rs 5,000 a month from age 25 to 35 and then stopping completely ends up with more at 60 than someone paying the same Rs 5,000 a month from 35 all the way to 60. The first pays in Rs 6 lakh. The second pays in Rs 15 lakh. At 8%, the first finishes with about Rs 67.14 lakh and the second with about Rs 47.55 lakh.

Two and a half times the money in, and a worse result. That gap is compound interest, and it's the reason the idea is worth understanding properly rather than as a slogan about the eighth wonder of the world.

What is compound interest?

Compound interest is interest calculated on the original amount plus every rupee of interest already added, so the balance it works on keeps growing. Simple interest never gets that treatment, which is the entire difference between the two.

Put Rs 1,00,000 in at 8%. Year one earns Rs 8,000. Year two is worked out on Rs 1,08,000, so it earns Rs 8,640. Year three runs on Rs 1,16,640 and earns Rs 9,331.

The rate never moved. Only the base did.

Each period the same three steps repeat: work out the interest on the current balance, add it to the balance, then use that larger balance next time. Everything else about compounding follows from those three steps, including the parts that look surprising later.

How do you calculate compound interest?

The compound interest formula is A = P x (1 + r/n) raised to the power n x t, where P is the principal, r is the annual rate as a decimal, n is how many times interest is added each year, and t is the number of years. When interest is added once a year, n is 1 and the whole thing collapses to A = P x (1 + r) to the power t.

Indian textbooks usually write it as A = P x (1 + R/100) to the power T, using the rate as a whole number. Same formula, different notation, same answer.

That gives you the final amount. For the interest on its own, subtract what you started with: CI = A minus P.

A one-time Rs 1,00,000 at different rates, compounded yearly:

Annual rate	After 10 years	After 20 years	After 30 years
4%	Rs 1,48,024	Rs 2,19,112	Rs 3,24,340
7%	Rs 1,96,715	Rs 3,86,968	Rs 7,61,226
10%	Rs 2,59,374	Rs 6,72,750	Rs 17,44,940
12%	Rs 3,10,585	Rs 9,64,629	Rs 29,95,992

Read across a row and you see time at work. Read down a column and you see the rate. Six percentage points between 4% and 10% produces a 1.75 times gap at ten years and a 5.4 times gap at thirty, which is the clearest demonstration that the two ingredients don't contribute equally.

For your own numbers, our compound interest calculator runs any starting amount, rate and horizon.

How much does compounding frequency actually change?

Compounding more often does increase the result, but by far less than most people expect: the whole distance from yearly to daily is worth about a third of a percentage point of effective rate. This is the single most over-estimated variable in the topic.

Rs 1,00,000 at 8%, held for ten years:

Interest added	Value after 10 years	Effective annual rate	Gained over yearly
Yearly	Rs 2,15,892	8.000%	Rs 0
Half-yearly	Rs 2,19,112	8.160%	Rs 3,220
Quarterly	Rs 2,20,804	8.243%	Rs 4,911
Monthly	Rs 2,21,964	8.300%	Rs 6,072
Daily	Rs 2,22,535	8.328%	Rs 6,642

Ten years of daily compounding beats ten years of yearly compounding by Rs 6,642 on a lakh. Worth having. Not worth reorganising your money over.

The detail I find genuinely surprising is at the bottom of that table. Daily compounding lands within Rs 19 of continuous compounding, which is the theoretical ceiling where interest is added at every instant. Once you're compounding daily, there's essentially nothing left to gain from compounding faster, because the series converges. So "compounds daily" is a real feature and a small one, and any product leaning hard on it is selling you a third of a percentage point.

Where it does matter is in comparing offers honestly. A 7.9% rate compounded monthly beats an 8% rate compounded yearly, because the first works out to an effective 8.19%. That's what the effective annual rate column is for.

Indian savings accounts sit oddly here. RBI requires interest on savings deposits to be worked out on a daily product basis, meaning on your end-of-day balance, but credited only at quarterly or longer intervals. So the calculation is daily and the compounding is quarterly.

What is the Rule of 72, and when does it break?

The Rule of 72 estimates doubling time by dividing 72 by the annual rate, and it is accurate to within a few weeks anywhere between 4% and 12%. At 8% it predicts 9 years against a true 9.01. Close enough to do in your head.

Rate	Rule of 72 says	Actually takes
4%	18 years	17.67 years
8%	9 years	9.01 years
12%	6 years	6.12 years
20%	3.6 years	3.80 years

It's most accurate right around 8% and drifts at the extremes. By 20% the shortcut is out by about five months, which matters if you're using it on credit card debt rather than savings. Underestimating how fast a 20% balance doubles is the wrong direction to be wrong in.

Why does time matter more than the rate?

Time beats rate over long horizons because compounding loads almost all of its gains into the final years, and only time can buy those years. The rate can be improved at any point. The years cannot be added back.

Take Rs 5,000 a month at 8%:

	Pays in	Ends at 60 with
Pays 25 to 35, then stops	Rs 6,00,000	Rs 67,14,280
Pays 35 to 60	Rs 15,00,000	Rs 47,55,132
Pays 25 to 60	Rs 21,00,000	Rs 1,14,69,412

The first saver puts in 40% of what the second does and finishes 41% ahead. Nothing separates them except a ten-year head start that stopped a quarter of a century before the finish line.

That's also the honest answer to a question people ask nervously, which is whether starting late means the chance is gone. It doesn't. A 40-year-old still has twenty years of compounding available, and twenty years is a great deal more than ten. The maths rewards early starts without punishing late ones.

How does compound interest work against you on debt?

The same mechanism runs in reverse on money you owe, and it runs fastest on credit cards because most of them compound daily. Nothing about the arithmetic changes. Only the direction the money travels.

An Indian credit card charging 3.5% a month gets quoted as 42% a year, which is just 3.5 multiplied by twelve. Count the monthly compounding, though, and the effective rate is 51.1%. That gap between the quoted number and the real one is this whole page in miniature, applied to a product millions of people carry.

A Rs 1,00,000 balance left untouched grows to Rs 1,51,107 after a year and Rs 2,28,333 after two.

Compare that with the savings side of this page, where 8% took about nine years to double a balance. At 51.1%, doubling takes 1.68 years.

There's a useful way to read that. Clearing a balance costing 51.1% removes a cost that's certain, and no ordinary investment offers a reliable 51.1% return to match it. Our simple interest explainer covers the flat-rate loans where the opposite trick is played, quoting a low number that hides a high one, and the two kinds of interest are set side by side in simple vs compound interest.

What this post deliberately does not cover

This explains what compound interest is, how the formula works, what compounding frequency is worth, and how the same mechanism behaves on debt. It isn't advice on where to put your money, which account or fund to choose, or how to prioritise saving against repaying a debt.

It also leaves out inflation, which quietly reduces every figure above in real terms, along with the tax treatment of interest, which differs by product and country and can change an after-tax result substantially. The examples assume a fixed rate held for the whole period, which no real market return and no floating-rate loan actually does, so treat them as illustrations of the mechanism and not forecasts. Anything touching your own tax position belongs with a chartered accountant, and for how a rate gets set and reset in the first place, see what an interest rate is.

Frequently asked questions

What is compound interest in simple terms?

Compound interest is interest calculated on the original amount plus every rupee of interest already added, so the balance it works on keeps growing. Put Rs 1,00,000 in at 8% and year one earns Rs 8,000. Year two is calculated on Rs 1,08,000, so it earns Rs 8,640. Year three earns Rs 9,331. Nothing about the rate changed. Only the base did. That is the whole idea, and it is why the growth line curves upward and not running straight like simple interest.

What is the compound interest formula?

The full formula is A = P x (1 + r/n) raised to the power n x t, where P is the principal, r is the annual rate as a decimal, n is how many times interest is added per year, and t is the number of years. When interest is added once a year, n equals 1 and it simplifies to A = P x (1 + r) to the power t. To get the interest alone rather than the final amount, subtract the principal: CI = A minus P. Indian textbooks often write the same thing as A = P x (1 + R/100) to the power T.

How much difference does daily compounding actually make?

Less than most people expect. On Rs 1,00,000 at 8% held for 10 years, yearly compounding produces Rs 2,15,892 and daily compounding produces Rs 2,22,535, a gap of Rs 6,642 across the whole decade. Daily compounding lands within Rs 19 of continuous compounding, which is the mathematical ceiling. Moving from yearly to daily raises the effective annual rate from 8% to about 8.33%, so frequency is worth roughly a third of a percentage point while the rate itself is worth whole points.

What is the Rule of 72?

The Rule of 72 estimates how long money takes to double under compound interest: divide 72 by the annual rate. At 8% it predicts 9 years and the true answer is 9.01 years. At 4% it predicts 18 years against a true 17.67, and at 12% it predicts 6 against a true 6.12. The approximation is at its best around 8% and loses accuracy at the extremes, so at 20% it predicts 3.6 years when the real figure is 3.8.

Why does starting early matter more than the interest rate?

Because compounding loads its gains into the final years, and only time can buy those years. Someone paying Rs 5,000 a month from age 25 to 35 and then stopping completely reaches about Rs 67.14 lakh by 60, having paid in Rs 6 lakh. Someone paying the identical Rs 5,000 a month from 35 to 60 pays in Rs 15 lakh, two and a half times as much, and reaches about Rs 47.55 lakh. The early saver contributed 40% as much and finished 41% ahead.

Does compound interest work against you on debt?

Yes, and credit cards are where it bites hardest. An Indian card charging 3.5% a month is quoted as 42% a year, which is simply 3.5 multiplied by twelve, but once the monthly compounding is counted the effective rate is 51.1%. A Rs 1,00,000 balance left untouched grows to Rs 1,51,107 after a year and Rs 2,28,333 after two, and doubles in 1.68 years. The mechanism is identical to a savings account. The only difference is the direction the money travels, which is why clearing a high-rate balance removes a cost no ordinary investment reliably matches as a return.

Sources

• Reserve Bank of India, Master Direction on Interest Rate on Deposits (Co-operative Banks), sections 6 and 11 (savings deposit interest calculated on a daily product basis and credited at quarterly or longer intervals) rbi.org.in
• Consumer Financial Protection Bureau, What is credit card interest? (how card interest compounds, including daily compounding) consumerfinance.gov
• U.S. Securities and Exchange Commission, Office of Investor Education, Compound Interest Calculator investor.gov
• Every figure in the tables is our own calculation, run directly from A = P x (1 + r/n) to the power n x t, with the doubling times solved from the same formula rather than taken from the Rule of 72.