The formula A = P(1 + r/n)^(nt) generalises simple interest by replacing the interest period of one year with a fraction of a year. With each compounding period, you apply a smaller rate (r/n) to a balance that includes prior interest. As n approaches infinity, the formula approaches continuous compounding A = P × e^(rt) - used in advanced finance but rarely in retail products. For everyday Indian banking, n is 1 (yearly), 2 (half-yearly), 4 (quarterly), 12 (monthly), 365 (daily) or 365.25 (continuous-like).
Indian fixed deposit calculations almost universally use quarterly compounding (n = 4). The rate quoted is annual; the bank divides by 4 each quarter, applies it, and adds it to the principal. This is why a 7% FD effectively yields about 7.19% over a year - the difference is the quarterly compounding bonus. Recurring deposits use the same quarterly compounding but applied to a series of monthly contributions, similar to a SIP but with a guaranteed rate.
For PPF the government compounds annually at the rate notified each quarter - so the 'compound' formula here applies but the rate may change between years. For EPF, interest is credited annually and the rate is announced after year-end. For credit cards, compounding is typically daily on the unpaid principal - which is what makes credit card debt so corrosive. Use this calculator with daily compounding and a 36% rate to see how a ₹1 lakh balance grows if you let it sit.
The Rule of 72 is a handy mental shortcut: divide 72 by the annual rate to estimate how many years it takes to double your money. At 8%, 72/8 = 9 years to double. At 12%, 72/12 = 6 years. The rule comes from a Taylor expansion of the compounding formula and is accurate within 1-2% for rates between 4% and 15%.