Compound Interest Calculator

The compound interest formula is: A = P × (1 + r/n)^n×t, where A is the final maturity amount, P is the principal (initial investment), r is the annual interest rate as a decimal (e.g. 8% = 0.08), n is the number of times interest compounds per year (monthly = 12, quarterly = 4, daily = 365), and t is the investment duration in years. The compound interest earned is CI = A − P. The key mechanism: at the end of each compounding period, the interest earned is added to the principal. In the next period, interest is calculated on this larger amount — "interest on interest." This positive feedback loop is what creates exponential growth over time. For example: ₹1,00,000 at 10% p.a. compounded monthly for 5 years: A = 1,00,000 × (1 + 0.10/12)^(12×5) = 1,00,000 × (1.00833)^60 = ₹1,64,533. Total CI = ₹64,533.

Simple Interest (SI) = P × r × t — calculated only on the original principal, constant each period. Compound Interest (CI) = P(1 + r/n)^(nt) − P — calculated on principal plus all accumulated interest, growing each period. For ₹1,00,000 at 10% for 10 years: SI = ₹1,00,000 (total ₹2,00,000). CI annual = ₹1,59,374 (total ₹2,59,374). CI monthly = ₹1,70,704 (total ₹2,70,704). The gap between CI and SI compounds with time. After 20 years at the same rate, CI annual gives ₹5,72,749 vs SI's ₹3,00,000 — CI generates 91% more wealth for the same principal and rate. Albert Einstein reportedly called compound interest the "eighth wonder of the world: he who understands it, earns it; he who doesn't, pays it" (most famously applied to debt, where you're on the wrong side of this equation).

For monthly compounding, use n = 12 in the formula: A = P × (1 + r/12)^12t. Step-by-step example for ₹50,000 at 8% p.a. monthly for 3 years: (1) Convert rate: r = 0.08. (2) Monthly rate = 0.08/12 = 0.006667. (3) Total periods = 12 × 3 = 36. (4) A = 50,000 × (1.006667)^36. (5) (1.006667)^36 = 1.27121. (6) A = 50,000 × 1.27121 = ₹63,560. (7) Monthly CI = ₹63,560 − ₹50,000 = ₹13,560. The monthly compounding formula is the standard used by most bank FDs in India that compound quarterly, and by all major loan EMI calculations. For loans/credit cards, you are on the paying side of this formula — compound interest works against you.

The Rule of 72 states: Years to double ≈ 72 ÷ Annual Interest Rate. It's a quick mental math approximation that works best for rates between 6% and 20%. At 6%: 72/6 = 12 years (exact: 11.9 years — 99.2% accurate). At 10%: 72/10 = 7.2 years (exact: 7.27 years — 99.0% accurate). At 12%: 72/12 = 6 years (exact: 6.12 years — 98.0% accurate). At 20%: 72/20 = 3.6 years (exact: 3.80 years — 94.7% accurate). At very high rates (30%+), use the Rule of 70 instead, which uses 69.3 for continuous compounding. The Rule of 72 is invaluable for quickly comparing investment options: at 6%, money doubles in 12 years; at 12%, it doubles in 6 years — and then doubles again in another 6 years, quadrupling in 12 years vs one doubling at 6%. This illustrates why earning 12% vs 6% is not "twice as good" — it's four times as powerful over a 12-year horizon.

Yes — compound interest is always better than simple interest for investments at the same nominal rate, because CI generates returns on previously earned returns while SI generates returns only on the original principal. The advantage grows exponentially with time. However, for loans and credit, compound interest works against the borrower — this is why credit card debt and personal loans with compound interest are so difficult to pay off. The mathematics cuts both ways: the same force that makes compound investing so powerful makes compound debt so destructive. This is why financial advisors universally recommend: (1) Invest in instruments with compound growth as early as possible. (2) Avoid compound-interest debt (credit cards, payday loans) unless absolutely necessary. (3) When borrowing, simple interest loans (rare, but exist) are less costly than compound interest loans at the same rate.

A Systematic Investment Plan (SIP) in a mutual fund uses compound interest (in the form of market returns) through two mechanisms: (1) Growth of each instalment: Each monthly SIP instalment stays invested and compounds for a different number of months — the first instalment compounds for the full period, the last for only one month. Over 20 years, the first instalment compounds for 240 months. (2) Rupee cost averaging: Investing fixed amounts monthly means buying more units when markets fall and fewer when they rise, reducing average cost per unit. The compound growth on a ₹10,000/month SIP at 12% CAGR over 20 years produces approximately ₹99.9 lakh from total invested capital of ₹24 lakh — a 4.2× multiplication. This is why SIPs in equity mutual funds are considered India's most accessible wealth-building tool for middle-class investors.

The Nominal Interest Rate is the stated annual rate without accounting for compounding within the year (e.g., 10% p.a.). The Effective Annual Rate (EAR), also called Annual Equivalent Rate (AER) or CAGR, is the actual annual rate after accounting for intra-year compounding: EAR = (1 + r/n)^n − 1. Examples at 10% nominal: Annual compounding: EAR = (1+0.10/1)^1−1 = 10.00%. Quarterly: EAR = (1+0.10/4)^4−1 = 10.38%. Monthly: EAR = (1+0.10/12)^12−1 = 10.47%. Daily: EAR = (1+0.10/365)^365−1 = 10.52%. When comparing financial products, always use EAR for apples-to-apples comparison. A bank offering 10% compounded quarterly has an EAR of 10.38%, which is directly comparable to another bank's 10.38% annual rate. Most Indian bank FD comparison tools and RBI benchmarks use EAR.

Inflation erodes the purchasing power of compound interest returns. The real (inflation-adjusted) return formula is: Real Return = [(1 + Nominal Return) ÷ (1 + Inflation Rate)] − 1. At 10% nominal return with 6% inflation: Real return = (1.10 ÷ 1.06) − 1 = 3.77% per year. This means ₹10 lakh growing to ₹67.3 lakh in 20 years at 10% is only worth ₹21.0 lakh in today's purchasing power. To generate meaningful real wealth through compounding, your investments must earn at least 4–5% more than inflation. In India, where CPI inflation averages 5–7%: Savings account (3.5%): real return −1.5% to −3.5% — wealth destruction. FD (7%): real return 0–2% — barely keeping pace. Equity mutual funds (12–14% long-term CAGR): real return 5–8% — genuine wealth creation. PPF (7.1%, tax-free): effective real return for 30% taxpayers is equivalent to ~4–5% real. Always invest with a real return target, not just a nominal one.