Lesson 3
Compounding explained
Compounding means interest is added to your balance and then earns interest itself. Over a few months it barely shows; over decades it does most of the work. The same arithmetic, running the other way, is what makes long loans expensive.
Simple versus compound
₹1,00,000 at 8% a year for 10 years:
- Simple interest (interest only on the original amount): 1,00,000 × (1 + 0.08 × 10) = ₹1,80,000.
- Compounded yearly: 1,00,000 × 1.0810 = ₹2,15,892.50.
The extra ₹35,892 is interest earned on earlier interest.
How often interest is added
The more often interest is added, the more of it earns interest. At a quoted 7% a year:
| Compounding | Effective yearly rate | ₹1,00,000 after 5 years |
|---|---|---|
| Yearly | 7.000% | ₹1,40,255.17 |
| Half-yearly | 7.122% | ₹1,41,059.88 |
| Quarterly | 7.186% | ₹1,41,477.82 |
| Monthly | 7.229% | ₹1,41,762.53 |
The effective yearly rate is (1 + R/k)k − 1, where k is the number of compounding periods in a year. It lets you compare options with different compounding on one scale.
Where you meet compounding
- Bank fixed deposits: SBI compounds interest quarterly for completed quarters on reinvestment deposits (Source: State Bank of India, checked 26 October 2026). See the FD calculator.
- Recurring deposits: ICICI Bank states RD interest is compounded quarterly (Source: ICICI Bank, checked 26 October 2026). See the RD calculator.
- PPF: interest is worked out monthly but credited at the end of each financial year, on 31 March (Source: National Savings Institute, Ministry of Finance (Department of Economic Affairs), checked 26 October 2026), so it compounds once a year. See the PPF calculator.
- Loans: EMI loans charge interest monthly on the balance; unpaid interest on a loan grows the debt the same way savings grow.
Monthly rates: two conventions
To turn a yearly rate into a monthly one, you can divide by 12 or take the twelfth root. At 12% a year, dividing gives 1% a month, which compounds to 1.0112 − 1 = 12.68% a year. The twelfth root gives 1.121/12 − 1 = 0.9489% a month, which compounds to exactly 12%. The standard EMI formula uses the divide-by-12 convention. Our SIP calculator uses the twelfth root so that the yearly return you type is the yearly return you get.
The rule of 72
A quick mental check: money roughly doubles in 72 ÷ (yearly rate) years. The exact figure is log 2 ÷ log(1 + R).
| Rate | Rule of 72 | Exact (yearly compounding) |
|---|---|---|
| 6% | 12.0 years | 11.90 years |
| 8% | 9.0 years | 9.01 years |
| 12% | 6.0 years | 6.12 years |
Sources
- Deposit Rates (how term deposit interest is compounded and calculated), last updated 15 October 2026. State Bank of India. Checked 26 October 2026.
- RD Calculator: how RD interest is calculated (formula and worked example). ICICI Bank. Checked 26 October 2026.
- Public Provident Fund Scheme, 2019 (G.S.R. 915(E), 12 December 2019, as amended by G.S.R. 290(E), 5 May 2020). National Savings Institute, Ministry of Finance (Department of Economic Affairs). Checked 26 October 2026.
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