Compound Interest Formula Explained – How Money Grows Over Time
Compound interest is often called the "eighth wonder of the world" by investors and financial advisors. Understanding how it works is the single most important financial literacy concept for building long-term wealth — whether you're saving, investing, or taking a loan.
What is Compound Interest?
Compound interest is interest calculated on both the initial principal AND the accumulated interest from previous periods. Unlike simple interest (which is calculated only on the original principal), compound interest grows exponentially. The longer the time period, the more dramatically the "interest on interest" effect manifests — making time the most powerful variable in wealth building.
The Compound Interest Formula
Where:
A = Final Amount
P = Principal (initial investment)
r = Annual Interest Rate (as decimal)
n = Number of compounding periods per year
t = Time in years
Compound Interest = A − P
Step-by-Step Example
You invest ₹1,00,000 at 10% per annum, compounded annually, for 10 years.
- P = ₹1,00,000 | r = 0.10 | n = 1 | t = 10
- A = 1,00,000 × (1 + 0.10/1)^(1×10)
- A = 1,00,000 × (1.10)^10
- A = 1,00,000 × 2.5937 = ₹2,59,374
- Compound Interest = ₹2,59,374 − ₹1,00,000 = ₹1,59,374
Compare with Simple Interest: ₹1,00,000 × 10% × 10 = ₹1,00,000. Compounding earned you ₹59,374 more!
Compounding Frequency Matters
The more frequently interest is compounded, the more you earn. Same ₹1,00,000 at 10% for 10 years:
- Annually (n=1): A = ₹2,59,374
- Quarterly (n=4): A = ₹2,68,506
- Monthly (n=12): A = ₹2,70,704
- Daily (n=365): A = ₹2,71,791
Most Indian bank FDs compound quarterly. Mutual funds compound daily (NAV-based).
The Rule of 72
A quick mental shortcut: divide 72 by your interest rate to estimate how many years it takes to double your money.
- At 6% (FD): 72/6 = 12 years to double
- At 12% (equity fund): 72/12 = 6 years to double
- At 15% (aggressive equity): 72/15 = 4.8 years to double
Simple Interest vs Compound Interest
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Calculation basis | Only principal | Principal + accumulated interest |
| Growth pattern | Linear | Exponential |
| Used for | Short-term loans | Long-term investments |
Frequently Asked Questions
Does SIP benefit from compound interest?
Yes. SIP in mutual funds benefits from compounding because returns are reinvested. Additionally, SIPs benefit from rupee cost averaging — buying more units when prices fall, fewer when they rise.
Is compound interest on loans bad?
Yes, for borrowers. Credit card debt at 36-42% compounded monthly grows devastatingly fast. This is why credit card debt should always be cleared fully each month.
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