What is Compound Interest?
Compound interest is interest calculated on both the initial amount you deposited (the principal) and the interest that has already been added to your account.
In plain terms: your interest earns interest.
This creates exponential growth — the longer money sits and compounds, the faster it grows. Albert Einstein reportedly called it the “eighth wonder of the world.” Whether or not he actually said it, the math is undeniable.
Simple Interest vs. Compound Interest
With simple interest, you always earn interest only on the original principal.
With compound interest, each period’s interest is added to the principal before the next calculation.
Example: ₹1,00,000 at 10% per year for 5 years
| Year | Simple Interest (₹) | Compound Interest (₹) |
|---|---|---|
| 1 | 1,10,000 | 1,10,000 |
| 2 | 1,20,000 | 1,21,000 |
| 3 | 1,30,000 | 1,33,100 |
| 4 | 1,40,000 | 1,46,410 |
| 5 | 1,50,000 | 1,61,051 |
After 5 years, compound interest gives you ₹11,051 more on the same investment. Over 30 years, the gap becomes enormous.
The Compound Interest Formula
A = P × (1 + r/n)^(n × t)
Final amount (principal + interest)
A
Principal (initial amount)
P
Annual interest rate as a decimal (e.g. 8% = 0.08)
r
Number of compounding periods per year
n
Time in years
t
Compounding Frequency Matters
More frequent compounding = more total interest. Here’s ₹1,00,000 at 10% annual rate for 5 years:
| Compounding | Formula | Final Amount |
|---|---|---|
| Annually | (1 + 0.10/1)^(1×5) | ₹1,61,051 |
| Quarterly | (1 + 0.10/4)^(4×5) | ₹1,63,862 |
| Monthly | (1 + 0.10/12)^(12×5) | ₹1,64,532 |
| Daily | (1 + 0.10/365)^(365×5) | ₹1,64,861 |
The difference between annual and daily compounding is about ₹3,800 on ₹1 lakh. Multiply this across larger sums and decades and it becomes significant.
Worked Example
A = P × (1 + r/n)^(n×t)
Scenario: ₹50,000 FD at 7.5% annual, compounded quarterly, 3 years
P = 50,000
r = 0.075
n = 4 (quarterly)
t = 3
A = 50,000 × (1 + 0.075/4)^(4 × 3)
= 50,000 × (1.01875)^12
≈ ₹62,570
Interest earned = ₹62,570 − ₹50,000 = ₹12,570
(vs. simple interest: ₹11,250 — compound earns ₹1,320 more)The Rule of 72
A quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money.
| Rate | Years to Double |
|---|---|
| 4% | 18 years |
| 6% | 12 years |
| 8% | 9 years |
| 12% | 6 years |
| 18% | 4 years |
So at 8% compound interest, ₹1 lakh becomes ₹2 lakh in roughly 9 years, ₹4 lakh in 18 years, ₹8 lakh in 27 years.
Why Starting Early is So Powerful
Time is the most powerful variable. Starting 10 years earlier beats investing 2.5× more money, as Ravi and Priya’s example shows.
Two investors each earn 12% per year:
₹6,00,000
Ravi invests
More than Priya
Ravi's corpus at 60
₹15,00,000
Priya invests
Less than Ravi
Priya's corpus at 60
- Ravi invests ₹5,000/month from age 25 to 35 (10 years), then stops. Total invested: ₹6,00,000.
- Priya invests ₹5,000/month from age 35 to 60 (25 years). Total invested: ₹15,00,000.
At age 60, Ravi has more money — despite investing less than half as much — because his money had 25 extra years to compound.
This is the core lesson: time is the most valuable input in the compound interest formula. Starting 10 years earlier beats investing 2.5x more money.
Use our Compound Interest Calculator to model your own scenario — adjust principal, rate, compounding frequency, and duration to see how your money grows over time.