In this guide
This guide explains the four ingredients of compound interest, the formula, a worked example, how it compares with simple interest, why time matters so much, and common mistakes.
- Principal, rate, time and compounding frequency
- The compound interest formula
- A worked example
- Simple vs compound interest
- Why time matters
What compound interest means
With simple interest, you earn interest only on the amount you originally deposited. With compound interest, each interest credit is added to your balance, and the next calculation is made on that larger balance. In short: interest earns interest.
The same principle works against you on debt. Unpaid credit card interest that is added to the balance is charged interest in turn, which is why compounding debt can grow quickly.
The four ingredients
Every compound interest calculation depends on four inputs.
- Principal (P): the amount you start with.
- Interest rate (r): the annual rate, written as a decimal in the formula (8% = 0.08).
- Time (t): the number of years the money stays invested.
- Compounding frequency (n): how many times a year interest is added — 1 for annual, 4 for quarterly, 12 for monthly.
The compound interest formula
A = P × (1 + r/n)^(n × t). A is the final amount, and the compound interest earned is A − P.
r/n is the rate for each compounding period, and n × t is the total number of periods. For annual compounding, the formula simplifies to A = P × (1 + r)^t.
A simple worked example
Suppose you invest ₹1,00,000 at 8% a year, compounded annually, for 10 years. A = 1,00,000 × (1.08)¹⁰ ≈ ₹2,15,892, so the compound interest earned is about ₹1,15,892.
With simple interest at the same rate, you would earn ₹8,000 every year — ₹80,000 over 10 years — for a total of ₹1,80,000. Compounding adds roughly ₹35,892 more, purely from interest earning interest. These figures are illustrative; real products have their own rates, rules and taxes.
Use the Compound Interest Calculator to see how your money can grow with your own principal, rate, period and frequency.Open the Compound Interest CalculatorSimple interest vs compound interest
The difference is small at first and grows with every year, because compound interest builds on a larger base each time.
| Basis | Interest calculated on | Value after 10 years | Growth pattern |
|---|---|---|---|
| Simple interest | Original principal only | ₹1,80,000 | Straight line |
| Compound interest | Principal plus past interest | ₹2,15,892 | Accelerating curve |
Why time matters most
Keep the same ₹1,00,000 at 8% compounded annually and only change the period: about ₹2,15,892 after 10 years, ₹4,66,096 after 20 years and ₹10,06,266 after 30 years. The second decade adds more than the first, and the third more than the first two together.
That is the real benefit of compounding: the longer money stays untouched, the more of the final value comes from growth rather than your original deposit. Withdrawing interest early interrupts this, because withdrawn interest no longer earns anything.
Compounding frequency also matters, but less than rate and time. How monthly, quarterly and annual compounding compare is covered in our guide on compounding frequency.
Compounding beyond deposits
The same idea underlies SIP projections, where each monthly instalment compounds for a different length of time — the SIP Calculator applies it to regular investments. For investments that grew unevenly, the CAGR Calculator works backwards from start and end values to the constant annual rate that would have produced the same result.
Common mistakes
Small slips in the formula create large errors over long periods.
- Using the percentage instead of a decimal in the formula (8 instead of 0.08).
- Forgetting to divide the rate by n and multiply the years by n.
- Comparing products on headline rate without checking compounding frequency.
- Assuming interest compounds when it is actually paid out.
- Ignoring tax on interest and inflation when judging real growth.
Conclusion
Compound interest rewards patience: interest added to your balance earns interest itself, and the effect accelerates with time. Know your principal, rate, period and frequency, run the numbers, and keep tax and inflation in mind before relying on the result.