Compound Interest and the Rule of 72, Explained Simply

Every calculator on this site, from the FD calculator to the SIP calculator, rests on one idea: interest earns interest. Most people have heard the phrase “power of compounding” without ever seeing the actual numbers, and most explanations stop at a formula. This guide shows what compounding does to a real sum year by year, why the interval of compounding matters more than people expect, and how the Rule of 72 lets you estimate doubling time in your head. The rule is a shortcut, and we check it against the exact calculation so you know how far to trust it.

All figures are produced by the same functions that run our calculators. The rates are assumed example rates, chosen to make the arithmetic clear; they are not any bank’s or fund’s rate.

Simple interest: the same amount every year

Simple interest is worked out on the original amount only. ₹1,00,000 at 8% simple interest earns ₹8,000 every year, for ever. After 10 years:

• Interest earned: ₹80,000
• Total: ₹1,80,000

That is what a non-cumulative FD does when it pays interest out every year and you spend it, and it is what most people picture when they hear “8% a year”.

Compound interest: interest joins the principal

In a cumulative deposit the ₹8,000 earned in year one is added to the deposit. In year two you earn 8% on ₹1,08,000, which is ₹8,640. In year three, 8% on ₹1,16,640. Each year’s interest is slightly bigger than the last. After 10 years of yearly compounding:

• Interest earned: ₹1,15,893
• Total: ₹2,15,893

The extra ₹35,893 is interest earned by earlier interest. Small over 10 years; not small over 20:

Read the last column downwards. The gap is tiny in the early years and then accelerates: compounding rewards time far more than it rewards amount. That is the “power” in power of compounding, and it is why the advice to start early is arithmetic, not a slogan.

The compounding interval: yearly, quarterly, monthly

“8% a year” can be credited once a year, every quarter or every month. The more often interest is added, the sooner it starts earning its own interest. Same ₹1,00,000, same 8%, same 10 years:

Indian banks compound term-deposit interest quarterly, which is why the quarterly row is what an FD actually pays, and why the FD calculator shows an “effective yield” slightly above the stated rate: 8% compounded quarterly behaves like 8.24% compounded yearly. The difference between quarterly and monthly is small; the difference between simple and any compounding is not.

The Rule of 72: doubling time in your head

How long does money take to double at a given rate? The exact answer needs a logarithm. The Rule of 72 replaces it with a division:

Years to double  ≈  72 ÷ annual rate (in %)

At 8%, 72 ÷ 8 = 9 years. At 12%, 6 years. At 6%, 12 years. It also runs backwards: to double in 10 years you need about 72 ÷ 10 = 7.2% a year.

The rule is an approximation, not a calculation. Here is how it compares with the exact doubling time, ln 2 ÷ ln(1 + r), for yearly compounding:

The rule is almost exact near 8%, slightly over-estimates at low rates and slightly under-estimates at high rates. For anything an Indian saver or investor will meet, from a 6% deposit to a 15% assumed equity return, the error is under a quarter of a year: good enough for a decision, not good enough for a statement of account. For a precise figure use the calculator.

A check with the lumpsum function of our SIP calculator, ₹1,00,000 at 8% compounded yearly:

• After 9 years (one doubling by the rule): ₹1,99,900, just short of ₹2,00,000 as the table predicts
• After 18 years (two doublings): ₹3,99,602, about 4×
• After 27 years (three doublings): ₹7,98,806, about 8×

Each doubling period multiplies the previous total, not the original one. Three doublings is 8 times, not 6 times, and that is the whole of the “power of compounding” in one line.

Compounding when you invest monthly: the SIP case

A SIP compounds in the same way, except that new money keeps arriving. At an assumed 12% a year, ₹5,000 a month:

The 30-year figure is not 3 times the 10-year figure; it is about 15 times. Doubling the monthly amount later does not catch up either: ₹10,000 a month for 20 years at the same rate gives ₹99,91,479, which is still well below ₹5,000 a month for 30 years (₹1,76,49,569). Ten extra years of compounding beat twice the money. (12% is an assumption, not a promise; equity returns vary widely from year to year. The point is the shape of the curve, which holds at any rate.)

Compounding works against you on loans

The same arithmetic runs in reverse when you owe money. A loan’s interest is charged on the outstanding balance every month, so an unpaid balance grows exactly the way a deposit grows. That is why a credit-card balance charged at, say, 3% a month (over 42% a year when compounded) doubles in roughly two years, and why prepaying a home loan early saves so much: you are removing principal before it can compound against you. Our EMI guide and prepayment guide show the numbers.

Common misunderstandings

• “8% for 10 years is 80%.” That is simple interest. Compounded yearly it is 115.9%, and compounded quarterly 120.8%.
• Using the Rule of 72 for a statement. It is a mental estimate. Deposit receipts, loan schedules and tax computations use the exact formula, and so do our calculators.
• Ignoring inflation. Money doubling in 9 years at 8% is less impressive if prices also rise. The real rate is roughly the nominal rate minus inflation, and the Rule of 72 works on that too: at a real 3%, purchasing power doubles in about 24 years.
• Ignoring tax. Interest on deposits is taxable each year, which lowers the effective compounding rate. For someone in the 30% slab, 8% before tax compounds at roughly 5.6% after tax, before cess.
• Thinking the rate matters more than the time. In the SIP table, going from 10 to 30 years multiplied the result by 15. No realistic change of rate does that.

The formulas

Simple interest:              A = P × (1 + r × t)
Compound, n times a year:     A = P × (1 + r/n)^(n × t)
Exact doubling time (years):  t = ln 2 ÷ ln(1 + r)       (yearly compounding)
Rule of 72 (estimate):        t ≈ 72 ÷ (r × 100)
P = principal, r = annual rate ÷ 100, t = years, n = compounding periods per year

Try your own amounts in the FD calculator (it lets you switch the compounding interval) and the SIP calculator.

Frequently asked questions

Is the Rule of 72 accurate? Within a few months of the exact figure for rates between about 4% and 15% with yearly compounding; most accurate near 8%. Use it for estimates, the calculator for decisions.

Why 72 and not 70 or 69? The exact constant for continuous compounding is 69.3 (100 × ln 2). 72 is used because it is close enough at common rates and divides neatly by 2, 3, 4, 6, 8, 9 and 12.

Does an FD compound monthly or quarterly? Banks in India compound term-deposit interest quarterly. Our FD calculator defaults to quarterly and lets you change it.

Does the Rule of 72 work for SIPs? Not directly, because new money keeps coming in. It applies to a sum invested once. Use the SIP calculator for instalments.

Is compound interest the same as CAGR? CAGR (compound annual growth rate) is the single yearly rate that would turn a starting value into an ending value over a period, assuming yearly compounding. It is the same formula run backwards: given A, P and t, solve for r.