The formula, and the thing it hides
A = P (1 + r/n)^(nt)
P is the principal, r the annual rate as a decimal, n the compounding periods per year, t the years.
What that expression hides is where the money comes from. Which is why this calculator shows the simple interest figure alongside it. The gap between the two is the only number that actually argues for compounding.
What the gap looks like
₹1 lakh at 12%, compounded yearly:
| Years | Simple interest | Compound | Difference |
|---|---|---|---|
| 5 | ₹1.60 L | ₹1.76 L | ₹16,000 |
| 10 | ₹2.20 L | ₹3.11 L | ₹91,000 |
| 20 | ₹3.40 L | ₹9.65 L | ₹6.25 L |
| 25 | ₹4.00 L | ₹17.00 L | ₹13.00 L |
For the first five years compounding looks like a rounding error. By year twenty-five it is the result — the original ₹1 lakh is 6% of the final figure, and interest-earning-interest is the rest.
This is why "start early" is not motivational advice. The last ten years of a long compounding period produce more than the first fifteen combined, and you cannot buy those years back later.
Compounding frequency matters less than you think
At 10% a year:
| Frequency | Effective annual rate |
|---|---|
| Yearly | 10.00% |
| Half-yearly | 10.25% |
| Quarterly | 10.38% |
| Monthly | 10.47% |
| Daily | 10.52% |
The step from yearly to quarterly is worth having. From monthly to daily is 0.05% — a rounding error dressed up as a feature in advertising. Rate and time dominate; frequency is a footnote.
The Rule of 72
Divide 72 by the annual rate to get the years to double. At 12%, roughly six years. At 8%, nine years. At 6%, twelve.
It is accurate enough for mental arithmetic and useful for a sanity check: if a scheme claims to double your money in three years, it is implying a 24% annual return, and you should want to know exactly how.
It works against you too
The same arithmetic runs in reverse on loan interest and on investment fees. A 1% annual expense ratio is not 1% of your returns — it compounds against your entire balance every year, and over decades it reaches lakhs. That is the same mechanism in this calculator, pointed the other way, and it is worth seeing in rupees: expense ratio calculator.