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Compound Interest

SSC JE · Quantitative Aptitude

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← Simple Interest Difference SI vs CI →

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Core Concept

Read this first — the foundation of the topic

→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 Rules and Properties

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

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Formula Block

Memorise — 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)...

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Exam Patterns

What examiners ask — read before attempting PYQs

⚡Powerful Shortcut for CI-SI Difference

1

Identify values - P = 8000, R = 15%, T = 2 years

2

Apply formula - A = P(1 + R/100)^T

3

A = 8000(1 + 15/100)²

4

A = 8000(1.15)²

5

A = 8000 × 1.3225 = Rs. 10,580

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.

1

Let principal = P, rate = R%

2

After 2 years: P(1 + R/100)² = 13,230

3

After 3 years: P(1 + R/100)³ = 15,214.50

4

Divide equation 2 by equation 1: (1 + R/100) = 15,214.50/13,230 = 1.15

5

Therefore, R/100 = 0.15, so R = 15%

6

Substitute in equation 1: P(1.15)² = 13,230

7

P × 1.3225 = 13,230

8

P = 13,230/1.3225 = Rs. 10,000 Time-Saving Trick: When amount after n years and (n+1) years are given, rate = [(Amount after (n+1) years / Amount after n years) - 1] × 100 Most Common Mistake: 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

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 Facts

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'
Effective annual rate for half-yearly compounding = (1 + R/200)² - 1
For small rates, approximate CI ≈ SI + (SI × R × T)/(200)
Population growth/decay and depreciation follow compound interest formula

🚀 60-Second Revision

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

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