Compound Interest: How Money Grows Over Time
Compound interest is the most powerful force in personal finance — Albert Einstein allegedly called it the eighth wonder of the world. Here's exactly how it works and how to use it.
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Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (calculated only on the principal), compound interest earns 'interest on interest' — creating exponential rather than linear growth over time. This distinction becomes dramatic over long periods.
What Is Compound Interest?
₹1,00,000 invested at 10% simple interest for 20 years grows to ₹3,00,000 (₹10,000 per year × 20 = ₹2,00,000 interest). The same amount at 10% compound interest (annually) grows to ₹6,72,750 — more than double. The difference is purely the effect of reinvesting interest each year rather than withdrawing it.
The Compound Interest Formula
A = P × (1 + r/n)^(n×t), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the time in years. For continuous compounding: A = P × e^(rt).
Calculate compound interest
See how your money grows with different rates, periods, and compounding frequencies.
Compounding Frequency Matters
| Frequency | n value | ₹1L at 10% for 10 years |
|---|---|---|
| Annual | 1 | ₹2,59,374 |
| Semi-annual | 2 | ₹2,65,330 |
| Quarterly | 4 | ₹2,68,506 |
| Monthly | 12 | ₹2,70,704 |
| Daily | 365 | ₹2,71,791 |
| Continuous | ∞ | ₹2,71,828 |
The Rule of 72: Quick Doubling Time
The Rule of 72 is a quick mental math shortcut: divide 72 by your annual interest rate to get the approximate number of years it takes to double your money. At 8%: 72/8 = 9 years. At 12%: 72/12 = 6 years. At 6%: 72/6 = 12 years. This rule is accurate within 1-2% for interest rates between 6% and 20%.
Compound Interest Working Against You (Debt)
Compound interest works equally powerfully in reverse. A credit card balance of ₹50,000 at 36% annual interest (typical in India), with only minimum payments made, will take over 10 years to pay off and cost over ₹2,00,000 in total interest — 4× the original debt. High-interest consumer debt is the most urgent financial emergency to address — the return on paying off 36% debt is guaranteed 36%.
Frequently Asked Questions
What is the difference between APR and effective annual rate?
APR (Annual Percentage Rate) is the stated annual rate. Effective Annual Rate (EAR) is the actual rate after accounting for compounding frequency. A 12% APR compounded monthly is an EAR of 12.68%. When comparing financial products, always compare EAR (also called AER or XIRR), not APR.
How long does it take to double money at 7% interest?
Using the Rule of 72: 72 ÷ 7 ≈ 10.3 years. More precisely, using A = P × (1.07)^t, setting A = 2P gives t = ln(2)/ln(1.07) = 10.24 years.