Infographics: Compound & Simple Interest

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Compound & Simple Interest
A comprehensive visual guide to mastering interest calculations for competitive 
examinations
What is Interest?
Interest is the cost 
charged by lenders on 
the principal loan 
amount4essentially 
the price of borrowing 
money over time.
Interest Rate Factors
Rates depend on 
inflation (money's 
changing value over 
time) and borrower 
credibility (risk of 
default).
Economic Impact
Minor interest rate 
changes create ripple 
effects across banking, 
finance, and the entire 
economy.
Simple Interest: The Basics
Simple interest is calculated on the original 
principal amount for the entire duration at a fixed 
rate. Once credited, it doesn't earn additional 
interest.
Key Formula
SI = (P × R × T) / 100
P = Principal Sum (original loan)
R = Rate of interest per annum
T = Time period in years
Total Amount = P + SI
Quick Example
Find SI on ¹68,000 at 
20% p.a. for 2 years
SI = (68,000 × 20 × 2) / 
100
= ¹ 27,200
Total Amount = 
¹68,000 + ¹27,200 = 
¹ 95,200
Compound Interest: Growth on Growth
In compound interest, interest itself earns interest after each time period4the 
foundation of modern banking and wealth accumulation.
Year 1
¹100 grows to ¹106 at 
6% interest
Year 2
¹106 earns interest, 
becomes ¹112.36
Year 3
¹112.36 compounds to 
¹119.10
Essential CI Formulas
Annual: A = P(1 + R/100)n
Half-yearly: A = P(1 + R/200)2n
Quarterly: A = P(1 + R/400)4n
Variable rates: A = P(1 + R¡/100)(1 + 
R¢/100)(1 + R£/100)
Advanced Concepts
Present Worth: PW = x / (1 + R/100)n
Rate when sum becomes x times: R 
= 100(x1/n 2 1)
Rate from two amounts: R = [(A¢ 2 
A¡) / A¡] × 100
Simple vs Compound Interest
Simple Interest
Calculated only on principal 
amount
Interest remains constant each 
period
Linear growth pattern
Easier calculations, predictable 
returns
Used in short-term loans and 
simple deposits
Compound Interest
Calculated on principal plus 
accumulated interest
Interest increases each period
Exponential growth pattern
More complex, higher long-term 
returns
Standard in savings accounts 
and investments
Special Applications
Depreciation
Assets lose value over 
time. Final value after 
depreciation:
A = A (1 2 r/100)t
Example: A ¹40,000 laptop 
depreciating at 30% 
annually becomes ¹19,600 
after 2 years.
Population Growth
Population changes follow 
compound interest 
patterns.
Growth: P¡ = P (1 + r/100)n
Decline: P¡ = P (1 2 r/100)n
Example: 125,000 growing 
at 2% annually reaches 
132,651 in 3 years.
Loan Instalments
Equal instalments formula 
for loan repayment:
P = X/(1+r/100)n + ... + 
X/(1+r/100)
Used when repaying loans 
in equal periodic amounts 
with compound interest.
Solved Problem: Investment Splitting
Problem Statement
Nitu invests ¹20,000 split across 
three banks:
¹8,000 at 5.5% in Bank A
¹5,000 at 5.6% in Bank B
Remaining at x% in Bank C
Combined annual interest equals 
5% of initial capital. Find annual 
interest if entire ¹20,000 invested 
only in Bank C.
Solution Approach
Step 1: Calculate individual interests
Bank A: (8,000 × 5.5 × 1)/100 = ¹440
Bank B: (5,000 × 5.6 × 1)/100 = ¹280
Step 2: Total interest = 5% of ¹20,000 = 
¹ 1,000
Step 3: Bank C interest = 1,000 2 440 2 280 = 
¹280
Bank C principal = ¹7,000, so rate = (280 × 
100)/(7,000 × 1) = 4%
Step 4: If entire ¹20,000 at 4%: (20,000 × 4 × 
1)/100 = ¹ 8 0 0
Practice Problem: Compound Growth
Challenge Question
A sum of ¹12,000 deposited at compound interest doubles in 5 years. After 20 
years, what will the amount become?
0 1
Establish the doubling relationship
¹24,000 = ¹12,000 × (1 + r/100)u
Therefore: (1 + r/100)u = 2
0 2
Calculate for 20 years
x = ¹12,000 × (1 + r/100)²p
x = ¹12,000 × [(1 + r/100)u] t 0 3
Substitute and solve
x = ¹12,000 × [2] t x = ¹12,000 × 16
0 4
Final answer
x = ¹ 1,92,000
The amount doubles every 5 years: 12K 
³ 24K ³ 48K ³ 96K ³ 192K
Quick Reference Guide
P×R×T/100
Simple Interest 
Formula
Calculate interest 
on principal only
P(1+R/10&
Compound 
Amount (Annual)
Principal grows 
exponentially
2n
Half-Yearly 
Compounding
Double the time 
periods
4n
Quarterly 
Compounding
Quadruple the time 
periods
Master the Mathematics
Understanding interest calculations is fundamental for SSC CGL quantitative aptitude. 
Practice diverse problems covering simple interest, compound interest, depreciation, 
and population-based scenarios to build speed and accuracy. Remember: compound 
interest problems often require recognizing exponential patterns, while simple 
interest focuses on linear relationships.
1
Identify the Type
Determine if the 
problem involves 
simple or compound 
interest based on 
whether interest 
compounds
2
List Given 
Information
Write down P 
(principal), R (rate), T 
(time), and what you 
need to find
3
Select the Right 
Formula
Choose from SI, CI 
annual, half-yearly, or 
special application 
formulas
4
Calculate Carefully
Substitute values accurately and 
compute step-by-step to avoid errors
5
Verify Your Answer
Check if the result makes logical 
sense given the problem context