The recurring deposit (RD) maturity formula calculates how a series of fixed monthly deposits grows into a lump sum, where each instalment compounds for a different length of time depending on when it was deposited. Unlike a fixed deposit's single lump sum, an RD's maturity value is the sum of every monthly instalment's own compounded future value.
Formula
FV = ฮฃ P ร (1 + r/n)^(n ร tโ), for k = 1 to total months, where tโ = (months remaining for instalment k) รท 12
| Variable | Meaning |
|---|---|
| FV | Maturity amount โ sum of all compounded instalments |
| P | Fixed monthly deposit |
| r | Annual interest rate (as a decimal, e.g. 7.1% = 0.071) |
| n | Compounding frequency per year (usually 4 = quarterly) |
| tโ | Remaining time in years for instalment k until maturity |
Worked Example
Depositing โน5,000 per month for 60 months (5 years) at 7.1% per annum, compounded quarterly (n = 4):
- The first instalment compounds for close to the full 60 months; the last instalment compounds for barely any time at all
- Summing the compounded future value of all 60 instalments: FV = โน3,60,615
- Total deposited: โน5,000 ร 60 = โน3,00,000
- Interest earned: โน3,60,615 โ โน3,00,000 = โน60,615
- Effective annual yield: 3.75%
Notice the effective yield (3.75%) is well below the nominal 7.1% rate โ that's expected for an RD, since the average instalment is invested for roughly half the 5-year tenure rather than the full period, unlike a lump-sum FD where the entire principal earns the full rate from day one.
Key Things to Know
- The formula requires summing every instalment separately โ there's no shortcut single-step calculation like there is for a lump sum, because each monthly deposit has a different remaining compounding period.
- Effective yield will always look lower than the nominal rate for an RD, purely due to the average holding time being shorter than the full tenure โ this isn't a sign of a bad deposit, it's just how recurring contributions work mathematically.
- Missing a monthly instalment typically triggers a small penalty at most Indian banks, and some also require making up the missed deposit โ this formula assumes every instalment is paid on schedule with no gaps.
- RD and FD use the same underlying compounding formula, just applied differently โ FD compounds one lump sum for the full tenure, RD compounds many smaller sums for their own remaining tenures.