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Compound Interest

Investment

Compound Interest

Interest calculated on both the initial principal and the accumulated interest from previous periods — making money grow exponentially over time.

Definition

Compound interest is interest calculated on both the initial principal and the interest that has already been earned in previous periods. Unlike simple interest (which is always calculated on the original principal alone), compound interest earns "interest on interest" — causing wealth to grow exponentially rather than linearly.

This is the fundamental mathematical principle behind all long-term wealth creation. Every mutual fund return, every bank FD, every PPF account, and every SIP calculator result is built on compound interest. The longer money compounds, the more dramatic the effect — a fact that makes starting early the single most powerful financial decision anyone can make.

The key variables in compounding are the principal, the interest rate, the compounding frequency, and most importantly, time. Of these, time is the variable that most investors underestimate.

Formula

A = P × (1 + r/n)^(n×t)

Where:

  • A = Final amount (principal + interest)
  • P = Principal (initial investment)
  • r = Annual interest rate (as a decimal)
  • n = Number of times interest compounds per year
  • t = Time in years

Compound Interest Earned = A − P

For continuous compounding: A = P × e^(r×t)

Worked Example

₹1,00,000 invested at 10% per annum for 10 years:

Simple interest: SI = ₹1,00,000 × 10% × 10 = ₹1,00,000. Final amount = ₹2,00,000.

Compound interest (annual): A = ₹1,00,000 × (1.10)^10 = ₹2,59,374

Compound interest (quarterly): A = ₹1,00,000 × (1 + 0.10/4)^40 = ₹2,68,506

The compound interest advantage over simple interest = ₹59,374. Over 20 years at the same rate, this grows to ₹3,72,750 in compound vs ₹3,00,000 in simple — a gap of ₹72,750 from the same principal.

Use the compound interest calculator to model any combination of rate, time, and compounding frequency.

Key Things to Know

  • The power of time: Starting 5 years earlier roughly doubles the final corpus at typical equity return rates (~12%). A 25-year-old investing ₹5,000/month until 60 (35 years) at 12% accumulates ₹3.24 crore. A 30-year-old doing the same for 30 years accumulates ₹1.76 crore — almost half, despite investing only ₹3 lakh less total. The missing 5 years cost ₹1.48 crore.
  • Compounding frequency matters less than you think: The difference between monthly and annual compounding at 8% over 10 years on ₹1 lakh is approximately ₹3,400. Far less than the difference made by adding even a small amount more to the principal. Don't obsess over compounding frequency — obsess over getting money invested as early as possible.
  • Negative compounding (debt): Compound interest works just as powerfully against you in debt. Credit card debt at 36–42% per annum compounds monthly. ₹50,000 unpaid for 3 years grows to approximately ₹1,62,000 — more than triple. This is why the minimum payment trap on credit cards is financially catastrophic.
  • CAGR vs fixed compound interest: Fixed deposits compound at a fixed rate. Mutual fund investments don't have a guaranteed rate — CAGR is the effective annualised return calculated retrospectively. When comparing returns, always compare on a CAGR basis to account for compounding properly.
  • Inflation compounds too: Inflation erodes purchasing power through the same compounding mechanism. ₹1 lakh today buys only ₹61,000 worth of goods in 10 years at 5% inflation. Your investment returns must compound faster than inflation for real wealth to grow — this is why equity (historically 12–15% CAGR in India) is essential for long-term wealth despite short-term volatility.

Related Calculators

Compound Interest Calculator →Calculate how your investment grows with compound interest. Get future value, total interest earned, and see the impact of regular contributions — free and instant.
SIP Calculator →Calculate your SIP returns instantly. Enter monthly investment, expected annual return, and time period to see total corpus, invested amount, and estimated gains.
Fixed Deposit Calculator →Calculate your FD maturity amount, total interest, and payout schedule instantly. Supports monthly, quarterly, and cumulative interest options for Indian bank FDs.

Related Terms

Simple InterestSimple InterestCAGRCompound Annual Growth RateSIPSystematic Investment PlanFuture ValueFuture Value (FV)
Frequently Asked Questions
What is the difference between compound interest and simple interest?
Simple interest is calculated only on the original principal — the interest earned each period is always the same. Compound interest calculates interest on both the principal and the previously accumulated interest — so each period's interest is larger than the last. Over long periods, the gap becomes enormous: ₹1 lakh at 10% simple interest grows to ₹2 lakh in 10 years; the same amount at 10% compound interest grows to ₹2.59 lakh.
What does compounding frequency mean?
Compounding frequency is how often interest is calculated and added to the principal. Annual compounding adds interest once a year. Monthly compounding adds interest 12 times a year. Daily compounding adds interest 365 times a year. More frequent compounding means your money grows slightly faster. Banks typically compound savings accounts daily and FDs quarterly. The difference between annual and daily compounding on ₹1 lakh at 8% for 10 years is approximately ₹4,500.
Why is compound interest called the eighth wonder of the world?
This phrase, often attributed to Albert Einstein (though disputed), captures the exponential nature of compounding. Early years of compounding show modest gains — but as the accumulated interest base grows, the absolute returns each year become enormous. ₹10,000 invested at 12% per year doubles in 6 years. That doubled amount (₹20,000) doubles again in another 6 years to ₹40,000 — without adding a single rupee. Time is the multiplier that makes compounding extraordinary.
How does SIP use compound interest?
A SIP (Systematic Investment Plan) in a mutual fund doesn't earn compound interest in the technical sense (it earns market returns, not a fixed rate). But the principle of reinvested gains works the same way: returns earned in early months stay invested and generate further returns. ₹10,000/month SIP for 20 years at 12% CAGR builds a corpus of approximately ₹99 lakh — even though total investment is only ₹24 lakh. The remaining ₹75 lakh is purely the compounding effect.
What is the Rule of 72?
The Rule of 72 is a quick mental calculation to estimate how long it takes to double money at compound interest: divide 72 by the annual interest rate. At 8%, money doubles in 72/8 = 9 years. At 12%, it doubles in 6 years. At 6%, it doubles in 12 years. This is an approximation — the actual doubling time uses logarithms — but it's accurate enough for practical planning and requires no calculator.