Core ConceptRead this first — the foundation of the topic
Compound Interest (CI) is the interest calculated on both the principal amount and the accumulated interest from previous periods. Unlike simple interest, compound interest grows exponentially because interest earns interest. This concept is fundamental in banking, investments, and loan calculations. Core Concept: When you deposit money in a bank, the bank pays you interest. In the second year, you earn interest not just on your original money, but also on the interest earned in the first year. This is compounding effect.
Key RulesCore rules you must know cold
1
Interest is added to principal at regular intervals (annually, half-yearly, quarterly)
2
Each period's interest is calculated on the new principal (original + accumulated interest)
3
The frequency of compounding affects the final amount
4
More frequent compounding means higher returns
Formula BlockMemorise — at least one formula appears in every paper
Amount = P(1 + R/100)^T
Compound Interest = Amount - Principal
Where P = Principal, R = Rate per annum, T = Time in years
For different compounding periods:
- Half-yearly: A = P(1 + R/200)^(2T)
- Quarterly: A = P(1 + R/400)^(4T)
- When rates differ: A = P(1 + R1/100)(1 + R2/100)(1 + R3/100)...
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL consistently asks 2-3 questions on compound interest. Common question types include finding amount after given years, comparing CI and SI, population growth problems, and depreciation calculations. Questions often involve 2-3 years timeframe with rates between 10-25%.
Powerful Shortcut for CI-SI Difference:
For 2 years: CI - SI = P(R/100)²
For 3 years: CI - SI = P(R/100)² × (300 + R)/100
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Identify values - P = 8000, R = 15%, T = 2 years
2
Step 2
Apply formula - A = P(1 + R/100)^T
3
Step 3
A = 8000(1 + 15/100)²
4
Step 4
A = 8000(1.15)²
5
Step 5
A = 8000 × 1.3225 = Rs. 10,580
6
Step 6
CI = Amount - Principal = 10,580 - 8000 = Rs. 2,580
Worked Example 2:
A sum becomes Rs. 13,230 in 2 years and Rs. 15,214.50 in 3 years at compound interest. Find the principal and rate.
ShortcutsUse these to save 30–60 seconds per question
When amount after n years and (n+1) years are given, rate = [(Amount after (n+1) years / Amount after n years) - 1] × 100
Most
Exam TrapsCommon mistakes students make — avoid these
Students frequently confuse the compounding frequency. When interest is compounded half-yearly, they forget to double the time period and halve the rate. Always remember: half-yearly means R/2 and 2T, quarterly means R/4 and 4T.
This single error costs marks in 40% of compound interest questions.
Another critical error is using simple interest formula for compound interest calculations, especially in word problems involving population growth or depreciation where the compounding effect is implicit.
Key Points to Remember
Amount formula: A = P(1 + R/100)^T where compound interest = A - P
For half-yearly compounding: A = P(1 + R/200)^(2T)
CI - SI for 2 years = P(R/100)² (most important shortcut formula)
CI - SI for 3 years = P(R/100)² × (300 + R)/100
When different rates apply: multiply (1 + R1/100)(1 + R2/100) for each year
Population growth and depreciation problems use compound interest concepts
More frequent compounding (quarterly vs annually) gives higher returns
If amount doubles in n years, it becomes 4 times in 2n years due to compounding
Rate finding trick: R = [(A₂/A₁) - 1] × 100 when consecutive year amounts given
Always convert compounding period: half-yearly means R/2 and time × 2
Exam-Specific Tips
Half-yearly compounding uses rate R/2 and time 2T in the formula
Quarterly compounding uses rate R/4 and time 4T in the formula
CI - SI difference for 2 years = P(R/100)²
CI - SI difference for 3 years = P(R/100)² × (300 + R)/100
When principal doubles, the time period is called 'doubling period'
A sum of ₹8,000 is invested at 10% per annum compound interest. What will be the amount after 2 years?
Practice 2easy
₹5,000 becomes ₹6,050 in 2 years at compound interest. What is the rate of interest per annum?
Practice 3easy
A principal amount doubles itself in 5 years at compound interest. In how many years will it become 8 times at the same rate?
Practice 4easy
₹10,000 is invested at 5% per annum compound interest compounded half-yearly. What is the amount after 1 year?
Practice 5easy
The difference between compound interest and simple interest on a sum for 2 years at 10% per annum is ₹100. What is the principal?
Practice 6easy
A sum of ₹4,000 is invested at 12% per annum compound interest. What will be the compound interest earned in 2 years?
Practice 7medium
A sum of ₹8,000 is invested at 10% per annum compound interest. What will be the amount after 3 years?
Practice 8medium
The compound interest on ₹5,000 at 8% per annum for 2 years is how much more than the simple interest for the same period?
Practice 9medium
At what rate per annum will ₹6,000 amount to ₹7,986 in 3 years at compound interest?
Practice 10medium
The difference between compound interest and simple interest on ₹10,000 at 5% per annum for 3 years is:
Practice 11medium
A sum of money doubles itself in 5 years at compound interest. In how many years will it become 8 times at the same rate?
Practice 12hard
A principal amount doubles itself in 5 years at compound interest. In how many years will it become 8 times itself at the same rate?
Practice 13hard
A principal amount invested at 20% per annum compound interest becomes ₹17,280 after 2 years. If the same principal is invested at 10% per annum simple interest, what will be the amount after 3 years?
Practice 14hard
A sum of money becomes ₹9,680 after 2 years at 10% per annum compound interest. What was the principal amount?
Practice 15hard
The difference between compound interest and simple interest on a sum for 3 years at 5% per annum is ₹244. What is the principal?
Practice 16hard
A certain sum becomes ₹6,050 in 2 years and ₹6,655 in 3 years at compound interest. What is the rate of interest per annum?
Practice 17hard
A sum of ₹12,000 is invested at compound interest. If the amount becomes ₹13,200 in 1 year and ₹14,520 in 2 years, what is the rate of interest, and how much interest is earned in the 2nd year?
60-Second Revision — Compound Interest
Formula: A = P(1 + R/100)^T, CI = A - P
Remember: Half-yearly = R/2 and 2T, Quarterly = R/4 and 4T
Shortcut: CI - SI for 2 years = P(R/100)²
Trap: Never confuse compounding frequency - adjust both rate and time
Trick: Rate = [(Next year amount / Current year amount) - 1] × 100
Pattern: Population and depreciation questions use CI formula
Quick check: CI should always be greater than SI for same P, R, T