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.
Interest is added to principal at regular intervals (annually, half-yearly, quarterly)
Each period's interest is calculated on the new principal (original + accumulated interest)
The frequency of compounding affects the final amount
More frequent compounding means higher returns
For different compounding periods:
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
Identify values - P = 8000, R = 15%, T = 2 years
Apply formula - A = P(1 + R/100)^T
A = 8000(1 + 15/100)²
A = 8000(1.15)²
A = 8000 × 1.3225 = Rs. 10,580
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.
Let principal = P, rate = R%
After 2 years: P(1 + R/100)² = 13,230
After 3 years: P(1 + R/100)³ = 15,214.50
Divide equation 2 by equation 1: (1 + R/100) = 15,214.50/13,230 = 1.15
Therefore, R/100 = 0.15, so R = 15%
Substitute in equation 1: P(1.15)² = 13,230
P × 1.3225 = 13,230
P = 13,230/1.3225 = Rs. 10,000
When amount after n years and (n+1) years are given, rate = [(Amount after (n+1) years / Amount after n years) - 1] × 100 Most
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.
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