How RD interest is calculated
A recurring deposit takes a fixed monthly instalment, but banks compound the interest quarterly, not monthly. The standard formula they use (matching what most RD calculators, including a bank's own, use) is:
where R is the monthly deposit, i is the quarterly interest rate (annual rate ÷ 4 ÷ 100), and n is the tenure in quarters (months ÷ 3).
The exponent of −1/3 in the formula is what accounts for deposits landing in different months of each quarter rather than all at the quarter's start — it's a standard interpolation, not an approximation we invented. Because compounding is quarterly while deposits are monthly, the exact figure a bank calculates can differ slightly from this formula depending on their day-count convention, but this is the widely used industry-standard method.
RD vs SIP vs FD
An RD is a bank deposit — the rate is fixed for the whole tenure and the amount is guaranteed by the bank (within deposit insurance limits), similar to an FD but funded monthly instead of as a lump sum. A SIP is a market-linked mutual fund investment — potentially higher returns over the long run, but not guaranteed and subject to market risk. An RD suits money you want to grow safely and predictably; a SIP suits money you're comfortable seeing fluctuate for potentially higher long-term growth.