Why RD's formula looks more complicated than FD's
An FD has one deposit compounding for one fixed period, so its formula is a single exponent. An RD has many deposits — one per month — each starting its own compounding clock on a different date. The RD maturity formula effectively sums up the compounded value of every individual monthly installment, which is why it has a more complex closed-form expression than FD's simple single-exponent formula, even though both use the same underlying quarterly-compounding convention.
The formula
maturityAmount = R × ((1+i)^n − 1) ÷ (1 − (1+i)^(−1/3)), where R is the fixed monthly deposit, i is the quarterly rate (annual rate ÷ 4 ÷ 100), and n is the tenure in quarters (tenure in months ÷ 3). This single formula is mathematically equivalent to separately compounding every individual monthly deposit for its own remaining time and summing all of them — it's just been algebraically simplified into one expression rather than requiring a month-by-month calculation.
A worked example, and why the total is less than it might seem
Depositing ₹5,000/month at 7% p.a. for 12 months totals ₹60,000 deposited, maturing to ₹62,310.66 — ₹2,310.66 in interest. Depositing the same ₹5,000/month for double the tenure, 24 months, totals ₹1,20,000 deposited, maturing to ₹1,29,098.90 — ₹9,098.90 in interest, nearly four times the interest of the 12-month RD for exactly double the deposits. This isn't a linear relationship because a longer tenure doesn't just add more deposits — it also gives every earlier deposit more total time to compound, so interest grows faster than the deposit total does as tenure increases.
Why the last deposit contributes almost no interest
The final monthly installment in an RD is made right before (or very close to) maturity, so it has essentially no time to earn any interest at all — nearly its entire contribution to the maturity amount is just its own face value. The first installment, by contrast, compounds for almost the entire tenure and contributes meaningfully more than its own face value. This uneven interest contribution across installments is the direct consequence of RD's staggered-deposit structure, and it's exactly why an RD earns less total interest than an FD holding the equivalent total principal from day one.
What stays constant regardless of tenure
The monthly deposit amount and the quoted annual rate stay fixed for the life of the RD — what changes with tenure is purely how many installments are made and how long each one has to compound. This predictability is part of RD's appeal as a disciplined savings vehicle: the eventual maturity amount for a given deposit amount, rate, and tenure is fully determined in advance, with no dependence on market performance.