Core ConceptRead this first — the foundation of the topic
The difference between Simple Interest (SI) and Compound Interest (CI) is one of the most frequently tested concepts in SSC CGL. This difference exists because compound interest includes interest on previously earned interest, while simple interest does not. Core Concept:
Simple Interest is calculated only on the principal amount throughout the investment period. Compound Interest is calculated on the principal plus accumulated interest from previous periods. The difference between CI and SI represents the 'extra earning' due to compounding effect.
Formula BlockMemorise — at least one formula appears in every paper
For 2 years: CI - SI = P × R² / (100)²
For 3 years: CI - SI = P × R² × (300 + R) / (100)³
Where P = Principal, R = Rate per annum, T = Time
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks three types of questions
(1) Direct calculation of difference given P, R, T (2) Finding principal when difference and rate are given (3) Finding rate when principal and difference are given. Most questions involve 2-3 years timeframe as longer periods make calculations complex
Powerful Shortcut for 2 Years
Difference = (SI for 1 year)² / Principal
This works because: If SI for 1 year = PRT/100, then difference = (PRT/100)² / P = PR²T²/(100²P) = PR²/100² (for T=2)
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Calculate SI for 2 years
SI = (P × R × T) / 100 = (8000 × 15 × 2) / 100 = Rs. 2400
2
Step 2
Calculate CI for 2 years
Amount = P(1 + R/100)ᵀ = 8000(1 + 15/100)² = 8000 × (1.15)² = 8000 × 1.3225 = Rs. 10,580
CI = Amount - Principal = 10,580 - 8000 = Rs. 2580
3
Step 3
Find difference
CI - SI = 2580 - 2400 = Rs. 180
Alternative (Using Formula):
CI - SI = P × R² / (100)² = 8000 × (15)² / (100)² = 8000 × 225 / 10000 = Rs. 180
ShortcutsUse these to save 30–60 seconds per question
for 3 Years:
For 3 years, the difference equals: 3 × (2-year difference) + (2-year difference × R/100)
Exam TrapsCommon mistakes students make — avoid these
Students often confuse the formula for different time periods. Remember: the 2-year formula is simplest and most tested. For 3 years, don't memorize the complex formula - use the relationship with 2-year difference instead.
Key Points to Remember
Difference exists only when time period is more than 1 year
For 2 years: CI - SI = P × R² / (100)²
For 3 years: CI - SI = P × R² × (300 + R) / (100)³
Difference represents interest earned on interest portions
2-year difference problems are most common in SSC CGL
If SI for 1 year is known, 2-year difference = (SI)² / Principal
Compound Interest is always greater than Simple Interest for same P, R, T
The difference increases exponentially with higher rates and longer periods
Exam-Specific Tips
For 2 years at 10% rate, difference is always 1% of principal
For 2 years at 20% rate, difference is always 4% of principal
For Rs. 100 at 15% for 2 years, difference is exactly Rs. 2.25
The ratio CI:SI for 2 years at 10% is always 21:20
For 3 years, minimum additional factor in formula is 300 (when R=0)
Difference for 2 years = P×R²/10000 (direct calculation)
For equal principal and rate, 3-year difference is roughly 3 times 2-year difference
At 25% rate for 2 years, difference equals 6.25% of principal
Practice MCQs
Difference SI vs CI — Practice Questions
11graded MCQs · easy to hard · full solution & trap analysis
A sum of ₹5,000 is invested at 10% per annum for 2 years. What is the difference between the compound interest and simple interest earned?
Practice 2easy
A principal of ₹10,000 is invested at 8% per annum. The difference between CI and SI for 3 years is:
Practice 3easy
If the difference between CI and SI on a sum at 12% per annum for 2 years is ₹144, what is the principal?
Practice 4medium
A principal amount becomes ₹11,664 after 2 years at 8% per annum compound interest. What would be the simple interest earned on the same principal for the same period at the same rate?
Practice 5medium
At what rate of interest per annum will the difference between compound interest and simple interest on ₹5,000 for 2 years be ₹50?
Practice 6medium
A sum of ₹8,000 is invested at 12% per annum. What is the difference between the compound interest and simple interest earned over 2 years?
Practice 7medium
A sum of money doubles itself in 5 years at simple interest. In how many years will it triple itself at the same rate of interest?
Practice 8medium
The compound interest on ₹4,000 for 2 years is ₹410. What is the rate of interest per annum, and what would be the simple interest for the same principal and period?
Practice 9hard
A principal amount becomes ₹6,050 in 2 years at 10% per annum under compound interest. What would be the simple interest on the same principal for the same period and rate?
Practice 10hard
The difference between the compound interest and simple interest on a sum for 2 years at 8% per annum is ₹64. If the same sum is invested for 4 years at the same rate, what is the difference between CI and SI?
Practice 11hard
A sum of ₹8,000 is invested at a certain rate per annum. After 2 years, the compound interest exceeds the simple interest by ₹80. What is the rate of interest per annum?
60-Second Revision — Difference SI vs CI
Formula: 2 years difference = P × R² / 10000
Remember: Difference exists only when T > 1 year
Trick: 2-year difference = (Annual SI)² / Principal
Pattern: Most SSC questions use 2-3 year timeframes
Trap: Don't use 3-year formula for 2-year problems
Quick check: At 10% for 2 years, difference = 1% of principal
Method: Calculate both CI and SI separately when formulas confuse