The formula
maturityAmount = Principal × (1 + annualRate/4/100)^(tenureMonths/3). The "/4" divides the annual rate into a quarterly rate, and "tenureMonths/3" converts the tenure into a number of quarters — because Indian bank FDs conventionally compound quarterly rather than annually, semi-annually, or as simple interest, even though the rate is always quoted as an annual percentage.
Why quarterly compounding beats simple interest at the same quoted rate
A ₹1,00,000 FD at 7% p.a. for 24 months matures to ₹1,14,888.18 under quarterly compounding — more than the ₹1,14,000 you'd get from plain simple interest (Principal × rate × years = 1,00,000 × 0.07 × 2). The ₹888.18 gap exists because quarterly compounding earns interest on previously earned interest starting from the very first quarter, not just on the original principal — a small but real difference that grows larger with longer tenures or higher rates.
Why tenure is measured in months, then converted to quarters
FD tenures are commonly quoted in months rather than years, since many FDs run for non-annual periods (6 months, 15 months, 18 months). Dividing the tenure in months by 3 converts it into a (possibly fractional) number of quarters — a 13-month FD, for example, works out to 4.33 quarters, and the exponent in the compounding formula simply uses that fractional value directly rather than rounding to a whole number of quarters.
The rate you're quoted vs the rate you actually earn
Because of quarterly compounding, the annual percentage yield (the effective rate you actually earn over a year) is always slightly higher than the quoted nominal annual rate — a 7% nominal rate compounded quarterly works out to an effective annual yield of about 7.19%, since each quarter's interest starts earning interest of its own for the rest of the year. This distinction between nominal and effective rate is standard across compound-interest products, not specific to FDs, but it's worth knowing when comparing an FD's quoted rate against another product's quoted rate that might compound differently.
What this calculation doesn't include
This is a pre-tax maturity calculation — it doesn't account for TDS (tax deducted at source) that banks apply once FD interest crosses the applicable annual threshold, or for the income tax ultimately due on that interest at your slab rate. The maturity amount shown is what the bank credits before any tax is withheld or separately assessed.