What is Compound Interest?
Interest earned on both your original principal and the interest already accumulated.
Compound interest means your returns earn returns. The more frequently it compounds (annually, quarterly, monthly) and the longer the horizon, the larger the effect — which is why starting early matters so much in investing.
Example
100,000 at 10% compounded annually for 20 years becomes about 672,750.
How compounding works
Compound interest is interest calculated on both your original principal and on the interest already added. The more often it compounds — yearly, quarterly, monthly, daily — the faster the balance grows. The effect is small at first and dramatic over long periods, which is why starting early matters more than investing large amounts later.
The rule of 72, and both directions
A quick shortcut: divide 72 by the annual rate to estimate the years for money to double — about 9 years at 8%. Compounding works powerfully for you inside savings and investments, and just as powerfully against you on credit-card and loan balances, where unpaid interest compounds into a larger debt.
The formula, step by step
Compound interest is calculated as A = P × (1 + r/n)n×t, where P is the principal, r is the annual interest rate (as a decimal), n is the number of times it compounds per year, and t is the number of years. A = the final amount. For example, with monthly compounding, n = 12: $10,000 at 6% compounded monthly for 10 years is P=10,000, r=0.06, n=12, t=10, giving A = 10,000 × (1 + 0.06/12)¹²⁰ ≈ $18,194 — about $1,194 more than the roughly $17,908 you'd get from the same rate compounded only annually, because interest is added to the balance 12 times a year instead of once.
A common mistake: confusing the nominal rate with the effective rate
A "6% annual rate" sounds like one number, but the actual return depends on how often it compounds. Compounded monthly, 6% nominal becomes an effective annual rate of about 6.17%; compounded daily, it edges up further. This is exactly why regulators require lenders to disclose an APR or APY rather than just a stated rate — two accounts or loans quoting the same headline percentage can cost or pay differently depending on compounding frequency, and comparing headline rates alone can be misleading. The mistake compounds (no pun intended) when people extend a short-term return into a long-term annualized figure without checking whether the underlying period actually compounds that way — a 1% monthly gain is not simply "12% a year," because compounding 1% twelve times actually yields about 12.68%. The gap between the two figures grows with the rate and the number of compounding periods, so it matters most for anyone comparing high-frequency returns like a monthly savings rate or a credit card's stated periodic rate against an annual benchmark.
How compound interest connects to EMI and amortization
Compound interest is the general principle; loan repayment applies a related but distinct version of it. A loan's EMI is calculated using compound interest on the reducing balance, and the amortization schedule is simply the month-by-month record of how that compounding plays out — interest first, on whatever principal is still outstanding, with the rest paying down the balance. A slower-amortizing, interest-heavy loan also takes longer to bring the loan-to-value ratio down through repayment alone, which is one reason lenders weigh both the rate and the repayment schedule, not just the headline number.
FAQ
Does compounding frequency actually make a big difference?
Less than most people expect. Going from annual to monthly compounding at the same stated rate raises the effective return, but the gap is small compared to the effect of rate or time — an extra 5–10 years invested, or a couple of percentage points of return, typically matters far more than whether interest compounds monthly or annually.
Is compound interest the same as APY or APR?
They're related but not identical. APY (annual percentage yield) is the actual annual return once compounding is factored in, so it's always ≥ the stated (nominal) rate. APR (annual percentage rate), used for loans, is a rate that may or may not fully reflect compounding depending on the country's disclosure rules — always check whether a quoted rate is nominal or already compounded before comparing two offers.