Simple & Compound Interest
SI earns the same every year. CI earns more each year as interest builds on top of interest.
A. What is Interest?
Principal (P)
The original amount of money borrowed or invested — before any interest is added.
ExampleYou put Rs.5000 in the bank. P = Rs.5000.
Rate (R)
The percentage charged as interest per year.
ExampleR = 8% means you earn Rs.8 for every Rs.100 per year.
Time (T or n)
How many years the money is kept or borrowed.
ExampleT = 3 years means interest is applied for 3 years.
Simple Interest (SI)
Interest calculated on the original principal only — every year you earn the exact same amount.
FormulaSI = (P × R × T) ÷ 100
Compound Interest (CI)
Interest calculated on principal + previous interest. The interest grows each year because the base gets bigger.
FormulaA = P × (1 + R/100)ⁿ then CI = A − P
B. Simple Interest
SI Formula Triangle — Cover What You Want to Find
Formula
SI = (P × R × T) ÷ 100
Amount = P + SI
Example 1 — Find SI: P=Rs.5000, R=8%, T=3 years
1SI = (5000 × 8 × 3) ÷ 100
2= 120000 ÷ 100 = Rs.1200
3Amount = 5000 + 1200 = Rs.6200
SI = Rs.1200 | Amount = Rs.6200
Example 2 — Find Rate: P=Rs.6000, SI=Rs.900, T=2 years
1Rearrange: R = (SI × 100) ÷ (P × T)
2R = (900 × 100) ÷ (6000 × 2) = 90000 ÷ 12000 = 7.5%
Rate = 7.5%
Example 3 — Find Time: P=Rs.4000, R=5%, SI=Rs.600
1Rearrange: T = (SI × 100) ÷ (P × R)
2T = (600 × 100) ÷ (4000 × 5) = 60000 ÷ 20000 = 3 years
Time = 3 years
C. Compound Interest
Formula
A = P × (1 + R ÷ 100)ⁿ
CI = A − P
n = number of years · raise (1 + R/100) to the power of n
Example 1 — P=Rs.1000, R=10%, n=2 years
1A = 1000 × (1 + 10/100)²
2= 1000 × (1.10)² = 1000 × 1.21
3A = Rs.1210
4CI = 1210 − 1000 = Rs.210
CI = Rs.210 | Amount = Rs.1210
Example 2 — Year-by-year: P=Rs.2000, R=10%, n=2
Y1Interest = 10% of 2000 = 200 → Balance = Rs.2200
Y2Interest = 10% of 2200 = 220 → Balance = Rs.2420
CI2420 − 2000 = Rs.420
CI = Rs.420 — Year 2 gave Rs.220 (more than Year 1's Rs.200)
⚠ Common mistakes:
(1) Forgetting to raise the bracket to the power n — A = P×(1+R/100)n not P×(1+R/100).
(2) CI is the interest only — it is A minus P. Students often give A as the answer when asked for CI.
(3) For Year 2 onwards, the base is the new balance, not the original principal.
D. SI vs CI — Key Difference
SI — Same every year
The interest amount stays the same every year because it is always calculated on the original principal.
Example — P=1000, R=10%
Year 1: Rs.100 Year 2: Rs.100 Year 3: Rs.100
Total SI after 3 years = Rs.300
Total SI after 3 years = Rs.300
CI — Grows every year
The interest grows each year because it is calculated on the increasing balance.
Example — P=1000, R=10%
Year 1: Rs.100 Year 2: Rs.110 Year 3: Rs.121
Total CI after 3 years = Rs.331 → bigger than SI!
Total CI after 3 years = Rs.331 → bigger than SI!
Key rule: For n=1 year, SI = CI. For n > 1 year, CI is always greater than SI for the same P, R, T.
Quick MCQ Revision
| Formula | Detail |
|---|---|
SI | (P × R × T) ÷ 100 |
Amount (SI) | P + SI |
CI Amount | P × (1 + R/100)ⁿ |
CI | A − P |
Find R from SI | (SI × 100) ÷ (P × T) |
| n > 1 year | CI always > SI |