Simple interest and compound interest are two of the most important ideas in money maths. They show up in school textbooks, bank exams, SSC and other competitive tests, loan agreements, fixed deposits and investments. The difference between them looks small over one or two years, but over a long time it becomes enormous. This guide explains both clearly, with worked examples, exam shortcuts and real-life uses.
Compare SI and CI for any principal, rate and time – with a year-by-year table.
Open the interest calculator →Simple interest: interest only on the principal
With simple interest, you earn (or pay) interest only on the original amount, called the principal. The interest is the same every year.
SI = P × R × T ÷ 100, where P is the principal, R the rate per year and T the time in years.
Example: ₹10,000 at 8% a year for 3 years.
- Interest each year: 10,000 × 8 ÷ 100 = ₹800.
- Total SI for 3 years: ₹800 × 3 = ₹2,400.
- Amount: ₹10,000 + ₹2,400 = ₹12,400.
Compound interest: interest on interest
With compound interest, the interest earned in each period is added to the principal, and the next period's interest is calculated on that larger amount. Your interest starts earning interest.
Amount = P × (1 + R ÷ 100)T (compounded yearly) and CI = Amount − P.
Same example, compounded yearly:
| Year | Opening amount | Interest at 8% | Closing amount |
|---|---|---|---|
| 1 | ₹10,000.00 | ₹800.00 | ₹10,800.00 |
| 2 | ₹10,800.00 | ₹864.00 | ₹11,664.00 |
| 3 | ₹11,664.00 | ₹933.12 | ₹12,597.12 |
CI = ₹12,597.12 − ₹10,000 = ₹2,597.12 – that's ₹197.12 more than simple interest, because each year's interest grows.
Compounding more often
Interest can be compounded half-yearly, quarterly or monthly. Divide the rate by the number of periods per year and multiply the time by it:
Amount = P × (1 + R ÷ (100 × n))n × T
For our ₹10,000 at 8% for 3 years: half-yearly gives ₹12,653.19, quarterly ₹12,682.42 and monthly ₹12,702.37. More frequent compounding means slightly more interest. Indian bank FDs usually compound quarterly – see how FD interest is calculated.
Why the difference grows over time
Over short periods, SI and CI are close. Over long periods, compounding pulls far ahead. ₹1,00,000 at 10% for 20 years:
- Simple interest: ₹10,000 a year × 20 = ₹2,00,000 interest, for a total of ₹3,00,000.
- Compound interest (yearly): 1,00,000 × 1.120 ≈ ₹6,72,750 – more than double the simple interest total.
The same idea explains why long-term investing works – and why long loans with compounding interest are so expensive. It's also why starting to save early matters more than saving a large amount later.
Doubling time
- Simple interest: money doubles when SI equals the principal, so
Time = 100 ÷ R. At 8%, that takes 12.5 years. - Compound interest: use the rule of 72 – about 72 ÷ R years. At 8%, about 9 years (exactly 9.01 years with yearly compounding).
Exam shortcuts: difference between CI and SI
Competitive exams often ask for the difference between compound and simple interest on the same principal (with yearly compounding):
- 2 years:
CI − SI = P × (R ÷ 100)². For ₹10,000 at 8%: 10,000 × 0.0064 = ₹64. - 3 years:
CI − SI = P × (R ÷ 100)² × (3 + R ÷ 100). For ₹10,000 at 8%: 64 × 3.08 = ₹197.12.
These save precious seconds in the exam hall. Practise a few, then check your answers with the calculator.
Where you see each in real life
| Simple interest | Compound interest |
|---|---|
| Some short-term personal and vehicle loans quoted at a "flat rate" | Fixed deposits (usually quarterly) |
| Short FDs under 6 months, and interest paid out regularly | Savings accounts, recurring deposits and PPF |
| Many textbook and exam problems | Credit card balances (which grow very fast if unpaid) |
Long-term investments like mutual funds don't pay a fixed interest rate, but their growth compounds in the same way – which is why their returns are usually described as a yearly CAGR.
A note on loans: a "flat rate" loan charges interest on the full original amount for the whole tenure, so its effective cost is much higher than a reducing-balance loan at the same quoted rate. Home loans and most bank loans use the reducing-balance method – see how EMI is calculated.
Frequently asked questions
What is the main difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus the interest already earned, so it grows faster.
What is the CI − SI formula for 2 years?
CI − SI = P × (R ÷ 100)², with yearly compounding. For ₹10,000 at 8%, the difference is ₹64.
Is compound interest always higher than simple interest?
For more than one compounding period and a positive rate, yes. For exactly one year compounded yearly, both are the same.
How long does money take to double at 8%?
About 12.5 years with simple interest, and about 9 years with yearly compound interest.