The Magic of Compounding

The question

"₹100 becomes ₹110 in a year. Fine. Why does everyone act like this is amazing?"

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Home reading

Interest, first

Put ₹100 in a bank that pays 10% a year. After one year the bank adds ₹10. You have ₹110.

That ₹10 is interest — the bank's payment for using your money. Nothing surprising yet.

Now the question nobody asks

In year two, does the bank pay you 10% of ₹100, or 10% of ₹110?

Of ₹110. Because ₹110 is what you now have. So year two adds ₹11, not ₹10.

That extra ₹1 looks trivial. It is the whole chapter.

Look down the interest column. It grows every year, and you did nothing. You are earning interest on your interest. That is compounding.

Why it feels slow and then does not

Compare two ways of growing money over 30 years, both at 10%, both starting with ₹1,000.

Simple interest — ₹100 added every year, always calculated on the original ₹1,000:

`` after 10 years ₹2,000 after 20 years ₹3,000 after 30 years ₹4,000 ``

A straight line. Every year adds the same ₹100.

Compound interest — interest calculated on whatever you have:

`` after 10 years ₹2,594 after 20 years ₹6,727 after 30 years ₹17,449 ``

Read those numbers again. In the first ten years compounding beats simple interest by about ₹594 — noticeable, not dramatic. By year thirty the gap is over ₹13,000.

Nothing changed in year twenty-five. The rule was the same the whole time. What changed is that the pile got large enough that 10% of it was a big number.

This is why compounding feels disappointing for years and then stops being disappointing. Most people quit during the boring part.

The three things that decide the outcome

1. Time — and it matters most

This surprises people, so look at it directly. Two people, both saving ₹1,000 a year at 10%:

• Meera starts at 20, stops at 30. She saves for 10 years only, ₹10,000 in total,

and never adds another rupee.

• Rohit starts at 30 and saves every year until 60. That is 30 years, ₹30,000 in

total — three times as much money.

At 60, Meera has more.

She put in a third of what he did and finished ahead, because her early rupees had forty years to compound and his later ones did not. Time did more work than money.

2. Rate

Higher rates compound faster, but be careful here — a higher promised return almost always means higher risk of losing it. Anyone promising a very high return with no risk is telling you something that is not true. Chapter 4 is about exactly those people.

3. Not interrupting it

Withdrawing money resets the effect. The pile has to stay whole for the pile to grow.

The rule of 72 — a trick worth memorising

To find roughly how many years money takes to double, divide 72 by the interest rate.

`` 72 ÷ 6% = 12 years 72 ÷ 8% = 9 years 72 ÷ 12% = 6 years ``

You can now do this in your head, in a shop, while someone is explaining a scheme to you. It is the fastest way to check whether a claim is even possible.

Compounding runs backwards too

Borrow at 36% a year — an ordinary rate on some credit cards and app loans — and the same mathematics works against you. By the rule of 72, what you owe doubles in about two years if you do not repay.

The same force that quietly builds savings quietly builds debt. Which side of it you stand on is one of the more consequential decisions in a life.

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Worked example

Your family saves ₹2,000 every month in an account paying 8% a year, and never withdraws.

`` after 5 years ₹1,47,000 (you deposited ₹1,20,000) after 10 years ₹3,66,000 (you deposited ₹2,40,000) after 20 years ₹11,78,000 (you deposited ₹4,80,000) ``

At 5 years, interest is about ₹27,000 — small beside your own deposits.

At 20 years, you have deposited ₹4.8 lakh and hold about ₹11.8 lakh. Roughly ₹7 lakh of that was never deposited by anyone. It is interest, and interest on interest.

(Figures rounded. Real accounts pay different rates and taxes apply — the shape is what matters, not the last rupee.)

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⚠️ The common mistake

"I will start later, when I have more money."

Meera and Rohit are the answer. Rohit saved three times as much and finished behind, because he began ten years later.

Compounding cannot be caught up with by trying harder afterwards. The years you did not use are simply gone, and no later amount replaces them. This is the one place in money where being early beats being rich.

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Check yourself

1. Why does year two pay more interest than year one, when the rate has not changed?
2. Use the rule of 72: at 9% a year, roughly how long does money take to double?
3. Meera saves ₹10,000 in total and Rohit ₹30,000, yet Meera ends with more. Explain in two

sentences.

1. A loan charges 36% a year. Roughly how long before the amount owed doubles?
2. Someone offers to double your money in one year. Using the rule of 72, what interest rate

is that? Say what you would ask them next.