Compounding on bank deposits
For a bank deposit, the quoted rate is only half the story. What you actually earn depends on how often the bank adds interest to your balance, and the difference between a nominal rate and its effective annual yield is what makes two 8% deposits pay differently.
Formula
Effective annual yield = (1 + r/n)^n − 1
- r — nominal annual rate as a decimal
- n — compounding periods per year
- Indian bank deposits typically use n = 4 (quarterly)
- Maturity = P × (1 + r/n)^(n × t)
Nominal rate versus effective yield
An 8% deposit compounded annually yields exactly 8%. Compounded quarterly it yields about 8.24%, and monthly about 8.30%. The bank has not changed its rate — it has changed how often the interest starts working for you.
This is why deposit advertisements show both a rate and an annualised yield. When comparing offers, compare effective yields, or you will pick the wrong deposit at least some of the time.
What it does over a decade
₹1 lakh at 8% for ten years grows to about ₹2.16 lakh with annual compounding, ₹2.21 lakh quarterly, and ₹2.22 lakh monthly. The same money on a simple-interest basis reaches only ₹1.80 lakh.
The advantage compounds on itself, so it widens with both the rate and the tenure. At 8% for twenty years, quarterly compounding produces roughly ₹4.87 lakh against ₹2.60 lakh under simple interest.
Tax quietly reduces your compounding
Deposit interest is taxable each year as it accrues, even in a cumulative deposit where you receive nothing until maturity. If you pay that tax from other income, the deposit compounds at the gross rate; if you fund it from the deposit, the effective compounding rate falls.
A 30%-bracket taxpayer earning 8% keeps roughly 5.5% after tax. Instruments with tax-free or deferred interest compound faster in the real world at the same headline rate.
The rule of 72 as a sanity check
Divide 72 by the rate for an approximate doubling time: nine years at 8%, twelve years at 6%. It is close enough to check any maturity figure at a glance.
Use the same rule on inflation. If prices double in twelve years at 6%, a deposit doubling in nine years at 8% is only modestly ahead before tax — and roughly level with inflation after it.
Example: ₹1 lakh at 8% for 10 years
- Compounded annually
- ≈ ₹2,15,892
- Compounded quarterly
- ≈ ₹2,20,804
- Compounded monthly
- ≈ ₹2,21,964
- Simple interest
- ₹1,80,000
- Effective yield (quarterly)
- ≈ 8.24%
- Effective yield (monthly)
- ≈ 8.30%
Frequency is worth about ₹6,000 over ten years on ₹1 lakh, while compounding itself is worth roughly ₹41,000 against simple interest.