The whole idea in one sentence
A rupee today is worth more than a rupee a year from now, because today's rupee can be put to work for a year and next year's cannot.
Everything else — compounding, discounting, present value, the arithmetic behind every loan and every SIP — is that sentence applied carefully.
It runs in both directions, and the second direction is the one people skip. Forwards: what is this money worth if left to grow? Backwards: what is a future amount worth in today's terms? The backwards question is how you compare a lump sum now against instalments later, which is the shape of most real financial decisions.
Why growth is not a line
Simple interest pays on the original amount. Compound growth pays on the original amount and on everything it has already earned, which is why the curve bends rather than sloping.
The bend is the whole story, and it arrives late. For the first several years, compound and simple growth look nearly identical — which is precisely the period during which people conclude it is not working and stop. The gap between the two widens slowly, then quickly, and almost all of the difference appears in the final third of any long horizon.
This is why patience is not a personality trait in investing. It is a requirement of the arithmetic. An investor who exits at year seven has paid the full cost of compounding — years of foregone spending — and collected almost none of the benefit.
The Rule of 72
A piece of mental arithmetic that is more useful than it has any right to be.
Divide 72 by the annual growth rate, and you get roughly the number of years it takes to double.
| Annual rate | 72 ÷ rate | Doubles in about |
|---|---|---|
| 4% | 72 ÷ 4 | 18 years |
| 6% | 72 ÷ 6 | 12 years |
| 9% | 72 ÷ 9 | 8 years |
| 12% | 72 ÷ 12 | 6 years |
| 18% | 72 ÷ 18 | 4 years |
It is an approximation and it is accurate enough for rates in the range people actually encounter. Two uses beyond the obvious:
Run it on inflation. At 6%, the Rule of 72 says prices double in about twelve years. That reframes a long-term goal faster than any spreadsheet.
Run it on debt. A balance costing 36% doubles in about two years if left alone. Applying the same tool to what you owe is uncomfortable and clarifying.
Why the first decade does most of the work
Here is the asymmetry that matters, and it is not the one usually stated.
Every rupee's contribution to a final corpus depends on how many doubling periods it gets. At 9%, money doubles roughly every eight years. So a rupee invested thirty-two years before you need it goes through roughly four doublings; a rupee invested sixteen years out goes through two.
Those are not twice as valuable. They are four times. Two extra doublings is a factor of four, not a factor of two — and this is the step intuition gets wrong, because we reason about time linearly and compounding is not linear.
The practical consequence is uncomfortable: the amount matters far less early on than the fact of starting. A small amount invested in your twenties can contribute more to a retirement corpus than a much larger amount invested in your forties, purely because of doublings available. Catching up later requires contributions large enough to substitute for time, and time is the cheaper input.
The backwards direction
Discounting is the same arithmetic run in reverse: what is a future amount worth today?
If money can grow at 9%, then ₹1,00,000 promised in eight years is worth roughly ₹50,000 today — because ₹50,000 invested now would become that amount. The future sum is not worth its face value; it is worth what you would need to set aside now to produce it.
This is the tool for any choice between money now and money later:
- A discount for paying upfront versus paying in instalments.
- A lump sum against a stream of payments.
- Any “guaranteed ₹X after twenty years” product — discount the promised amount back and see what return is actually being offered. It is frequently far less impressive than the headline number, which is why the headline is stated as a total rather than as a rate.
Do it in real terms
One correction that changes conclusions.
All of the above works in nominal terms and answers a question about rupees. What you care about is purchasing power, so the honest version subtracts inflation first and compounds the real rate.
At 11% nominal with 6% inflation, the real rate is roughly 5% — and the Rule of 72 now says purchasing power doubles in about fourteen years rather than the nominal seven. Same investment, honest answer.
Every projection that ignores inflation overstates what it is offering, and long projections overstate it enormously, because the error compounds too.
Testing it against real history
The arithmetic above assumes a steady rate. Nothing delivers a steady rate, and the difference between a smooth projection and a real path is exactly what determines whether somebody stays invested long enough for any of this to apply.
FNOTrader's Mutual Funds app runs contribution schedules against actual NAV history — around 34 million NAV rows — reporting XIRR alongside the maximum drawdown along the way, and rolling returns across every start date rather than one flattering window. A projection tells you what compounding can do; the drawdown tells you what you would have had to sit through to collect it.
Common questions
What is the time value of money?
The principle that a rupee today is worth more than a rupee later, because today's rupee can be put to work in the meantime. Compounding, discounting and present value are all applications of that one idea.
What is the Rule of 72?
A mental shortcut: divide 72 by the annual growth rate to get roughly the number of years it takes for money to double. At 9% that is about eight years, at 12% about six. It is an approximation and accurate enough for the rates people actually encounter.
Can I use the Rule of 72 for inflation and debt?
Yes, and both are more revealing than the usual use. At 6% inflation prices double in about twelve years; a balance costing 36% doubles in about two years if left alone.
Why does starting early matter so much?
Because value depends on the number of doubling periods, not on elapsed time. At 9%, money invested thirty-two years out gets roughly four doublings and money invested sixteen years out gets two — a factor of four, not a factor of two.
Can I make up for starting late by investing more?
Partly, but the arithmetic is unfavourable. Contributions have to be large enough to substitute for missing doubling periods, and time is the cheaper input — which is why the fact of starting matters more early on than the amount does.
What is discounting?
The time value of money run backwards: what a future amount is worth today. It is the tool for comparing a lump sum now against payments later, and for checking what return a 'guaranteed ₹X after twenty years' product is actually offering.
Should I use nominal or real returns in these calculations?
Real, for anything long term. Subtract inflation first and compound the real rate — at 11% nominal with 6% inflation, purchasing power doubles in roughly fourteen years rather than the seven the nominal figure suggests.
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