How compounding builds an amount you did not deposit
Why the same rate produces wildly different results over time, what compounding frequency is actually worth, and the rule of 72 and its limits.
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In short
- ₹1 lakh at 10% is ₹2.59 lakh after ten years and ₹17.45 lakh after thirty. The rate never changed; only the base did.
- Simple interest on the same deposit gives ₹4 lakh after thirty years. The ₹13.45 lakh difference is interest earning interest.
- Compounding frequency matters much less than people assume. Daily instead of yearly on ₹1 lakh at 10% for ten years is worth about ₹12,400.
- The rule of 72 gives the doubling time in your head and is accurate to within a few months for rates between 6% and 12%.
- Compounding works identically against you. Credit card interest at 42% a year doubles a balance in about twenty months.
Compound interest is interest calculated on the original amount and on the interest already added. That single sentence is the entire difference between it and simple interest, and over long periods it is the difference between a modest gain and a very large one.
A = P × (1 + r ÷ n)^(n × t)
where P is the principal, r the annual rate as a decimal, n the compounding periods per year and t the years.
What the difference actually looks like
₹1,00,000 at 10%, compounded annually against simple interest:
| Years | Compound | Simple | Difference |
|---|---|---|---|
| 1 | ₹1,10,000 | ₹1,10,000 | ₹0 |
| 5 | ₹1,61,051 | ₹1,50,000 | ₹11,051 |
| 10 | ₹2,59,374 | ₹2,00,000 | ₹59,374 |
| 20 | ₹6,72,750 | ₹3,00,000 | ₹3,72,750 |
| 30 | ₹17,44,940 | ₹4,00,000 | ₹13,44,940 |
In the first year they are identical, because there is no accumulated interest to earn on yet. By year thirty the compound figure is more than four times the simple one.
The shape of that column is the thing worth internalising. Nothing accelerates — the rate is 10% throughout — but the amount 10% is applied to keeps growing, so each year adds more than the last. In year one the deposit earns ₹10,000. In year thirty it earns ₹1,58,631.
This is why the last years of a long investment produce most of the money, and why an investment interrupted near its end loses far more than the elapsed time suggests.
Compounding frequency is worth less than you think
More frequent compounding gives a higher result, but the effect is small and it saturates quickly. On ₹1,00,000 at 10% for ten years:
| Compounding | Maturity | Effective annual rate |
|---|---|---|
| Yearly | ₹2,59,374 | 10.000% |
| Half-yearly | ₹2,65,330 | 10.250% |
| Quarterly | ₹2,68,506 | 10.381% |
| Monthly | ₹2,70,704 | 10.471% |
| Daily | ₹2,71,791 | 10.516% |
Going from yearly to daily is worth ₹12,417 over ten years — about 4.8% more. Going from 10% to 10.5% would achieve almost the same thing with annual compounding.
The practical lesson is to compare products on their effective annual rate, not their nominal rate and frequency separately. A 10.4% deposit compounded annually beats a 10.2% one compounded monthly, and the headline numbers suggest the opposite.
Continuous compounding — the theoretical limit, A = P × e^(rt) — gives ₹2,71,828 on the same deposit. That is the ceiling, and daily compounding is already within ₹37 of it. Frequency has very little left to give.
The rule of 72
Divide 72 by the annual rate for the approximate doubling time in years.
| Rate | Rule of 72 | Actual |
|---|---|---|
| 4% | 18.0 years | 17.7 |
| 6% | 12.0 years | 11.9 |
| 8% | 9.0 years | 9.0 |
| 10% | 7.2 years | 7.3 |
| 12% | 6.0 years | 6.1 |
| 20% | 3.6 years | 3.8 |
It is accurate to within a couple of months across the range that matters and drifts at high rates, where 69.3 divided by the rate is closer.
Its real use is as a mental check on claims. An investment promising to triple in three years implies a return above 44% a year, which should prompt a question about how. A scheme "doubling your money in five years" is offering roughly 14.4%, which is plausible for equity and not plausible for anything described as guaranteed.
Compounding against you
The formula does not care which direction the money flows.
Credit card revolving balance. A typical Indian card charges 3.5% a month, which is not 42% a year — monthly compounding makes it 51.1% effective. A ₹1,00,000 balance left untouched becomes ₹1,51,107 after a year and ₹2,28,333 after two. Paying only the minimum, usually 5%, can leave a balance outstanding for years.
Loans generally. An EMI schedule is compound interest solved for the payment. It is why the early instalments of a home loan are almost entirely interest, and why a prepayment made in year three saves far more than the same amount in year fifteen.
Fees. An expense ratio is a small negative compounding rate. 1.5% a year against 0.5% on ₹10 lakh over thirty years, at 12% gross, is a difference of about ₹62 lakh in the final value — ₹2.62 crore against ₹2.00 crore. The percentage is small and the compounded effect is not.
Inflation is compounding too
At 6% inflation, prices double every twelve years. Money kept still therefore halves in value on the same schedule.
This is why a nominal return has to be compared against inflation before it means anything. A guaranteed 7% deposit, taxed at 30% and set against 5% inflation, produces a real return close to zero: the balance grows and the purchasing power does not.
The number to model, for anything held longer than a few years, is the real return — approximately the nominal rate minus the inflation rate. It is smaller and less impressive than every projection implies, and it is the only one that predicts what the money will buy.
Where the calculator's assumptions bind
The rate is constant. Real returns are not, and the order in which good and bad years arrive changes the outcome even when the average is identical. A poor year early costs less than a poor year late, because the loss is applied to a smaller balance.
Nothing is added or withdrawn. A withdrawal removes not just the amount but everything it would have gone on to earn — which, thirty years out, is a multiple of the amount itself.
Tax is excluded. Interest taxed annually at your slab rate compounds on the post-tax amount, which is materially different from compounding on the gross. A tax-deferred or tax-free instrument compounds on the full amount, and over long periods that difference outweighs a percentage point of return.
The one thing that actually matters
Across every table above, the variable doing the most work is time, not rate.
₹1,00,000 at 10% for thirty years gives ₹17.45 lakh. The same amount at 12% for twenty-five years gives ₹17.00 lakh — a better rate, five fewer years, and a slightly worse outcome. Starting earlier is worth more than choosing better, and it is the only one of the two you can be sure of doing.
Nominal, effective and the rate you are quoted
Three different numbers travel under the word "rate", and lenders and banks are not obliged to use the same one as each other.
Nominal annual rate is the headline: 12% a year, compounded monthly. It is the periodic rate multiplied by the number of periods, and it is not what you earn or pay.
Effective annual rate folds the compounding back in. 12% compounded monthly is 12.68% effective. This is the number that makes two products comparable.
Annual percentage rate on a loan adds mandatory fees to the effective rate, which is why the APR on a personal loan with a 2% processing fee is meaningfully above its interest rate. Indian lenders must disclose it in the key facts statement.
| Nominal | Compounding | Effective |
|---|---|---|
| 12% | Yearly | 12.00% |
| 12% | Quarterly | 12.55% |
| 12% | Monthly | 12.68% |
| 12% | Daily | 12.75% |
The gap widens with the rate, which is why it matters most exactly where the stakes are highest. A credit card quoting 3.5% a month is quoting a 42% nominal rate and charging 51.1% effective — the nine-point difference is compounding, disclosed nowhere on the statement.
When comparing anything, convert both sides to an effective annual rate first. It takes one calculation and it removes the only variable that marketing material is free to choose.
What this calculator assumes
- A single principal, compounded at the frequency you select, with nothing added or withdrawn during the term.
- A constant annual rate across the whole term.
- Figures are before tax and before any charges.
- The term is measured in years; fractional years compound proportionally.
- Inflation is not applied, so the result is in future currency rather than today's purchasing power.