Compound vs Simple Interest, Effective Rates and the Rule of 72

₹1,00,000 at 8% for 5 years earns ₹40,000 in interest under one formula and about ₹46,933 under the other — same principal, same rate, same time, a real difference because of how the interest itself is treated. This is the mechanic behind loans, deposits, and investment projections across the site, so it's worth having straight once rather than re-deriving it every time a calculator uses it.

Two formulas

Simple interest is calculated on the original principal only, every period, so it grows in a straight line: Interest = (P × r × t) ÷ 100, where P is the principal, r is the annual rate as a percentage, and t is the time in years. A ₹50,000 principal at 6% for 3 years earns exactly (50,000 × 6 × 3) ÷ 100 = ₹9,000, whether you check after year 1, 2, or 3 — the same ₹1,800 accrues every single year.

Compound interest is calculated on the principal plus whatever interest has already accumulated, so each period's interest itself starts earning interest: A = P × (1 + r/n)^nt, where n is how many times per year interest compounds and A is the final amount. ₹1,00,000 at 8% compounded annually for 5 years grows to 1,00,000 × 1.08⁵ ≈ ₹1,46,933 — interest earned of about ₹46,933, versus the ₹40,000 simple interest would give at the same rate and term. The gap between the two widens the longer the money sits and the higher the rate, because compounding is fundamentally exponential growth while simple interest is linear.

Try the Simple Interest and Compound Interest calculators side by side with the same numbers to see this gap directly.

Compounding frequency: more often means a bit more

"8% annually" and "8% compounded monthly" aren't the same 8% — the more often interest is credited within the year, the sooner each installment of interest starts earning its own interest, so a higher compounding frequency produces a slightly larger result for the identical quoted annual rate. The effect is real but usually modest:

• 7% compounded quarterly behaves like about 7.19% compounded once a year.
• 8% compounded monthly behaves like about 8.30% compounded once a year.
• 12% compounded monthly behaves like about 12.68% compounded once a year.

This is exactly why an Indian bank FD, which typically compounds quarterly, produces a slightly higher maturity value than the same quoted rate compounded only annually would — see the FD Calculator's own worked example, which shows both side by side on the same deposit.

Nominal rate vs. effective annual rate

The "nominal" rate is the quoted annual percentage before accounting for compounding frequency. The "effective annual rate" is what that nominal rate actually works out to once compounding is factored in — the 7.19%, 8.30%, and 12.68% figures above are all effective rates for their respective nominal ones. This distinction is what makes two loans or deposits quoted at the same nominal percentage but different compounding frequencies not directly comparable without converting one to match the other — the same underlying idea that makes a flat-rate loan quote and a reducing-balance loan quote incomparable at face value, covered in more depth in the EMI flat vs. reducing rate guide.

Rule of 72: a fast estimate, not exact math

Roughly how long does it take an amount to double at a given compound rate? Divide 72 by the rate. At 8%, that's 72 ÷ 8 = 9 years — remarkably close to the true, exact answer of about 9.01 years. The rule trades a small amount of accuracy for arithmetic simple enough to do in your head, and how much accuracy it trades away depends heavily on the rate:

The rule is most accurate in roughly the 6–10% range, which is also where it's most commonly applied — for typical savings and investment rates. At low single-digit rates or rates above 15–20%, the gap grows large enough to matter, and it's worth running the exact formula through the Compound Interest Calculator instead of relying on the shortcut.

Inflation: the rate that matters is the one left over

A compound or effective rate tells you how fast a balance grows in the currency you counted it in — it says nothing about what that balance can actually buy later. If prices are also rising, part of that growth is just keeping pace with inflation rather than adding real purchasing power. A rough "real" (inflation-adjusted) rate is approximately your nominal rate minus the inflation rate — an 8% return with 5% inflation leaves roughly 3% of genuine growth in purchasing power, not the full 8%. None of the calculators on this site subtract inflation automatically; it's a separate adjustment to make on top of whatever growth rate they project.

Where these formulas stop applying

• A rate that changes mid-term. Every formula here assumes one fixed rate for the whole period. A floating-rate loan, a savings account whose rate the bank revises, or a government-notified rate like PPF's (reviewed every quarter) can all change partway through — the formulas describe what happens at a given fixed rate, not what happens if that rate moves.
• Taxes and fees. None of these formulas deduct tax on interest earned or account fees — both calculators here compute pure, pre-tax growth at the rate you enter.
• Market-linked returns. Compound interest assumes a known, constant rate. A mutual fund SIP or any market-linked investment doesn't have a guaranteed constant rate at all — the projected return is an assumption you supply, not a contracted number. The SIP projections guide covers that distinction and what a SIP projection does and doesn't promise.

For how compound interest plays out in three specific, real Indian savings products with their own particular deposit patterns and compounding rules, see how FD, RD, and PPF each apply these mechanics differently.