SIMPLE AND COMPOUND INTEREST
CSAT
Simple Interest and Compound Interest are important topics in CSAT because they test an aspirant’s understanding of money, time, and rate relationships. Questions are usually framed in a very practical manner, such as loans, savings, banking, and growth of money over time. CSAT does not demand heavy calculations; instead, it focuses on conceptual clarity and logical comparison between Simple Interest (SI) and Compound Interest (CI).
BASIC TERMINOLOGY
Principal (P)
• The original amount of money borrowed or invested
Rate of Interest (R)
• The percentage charged or earned on the principal per year
Time (T)
• Duration for which money is borrowed or invested
• Usually expressed in years
Interest
• Extra money paid or earned over the principal
SIMPLE INTEREST (SI)
Meaning
• Interest calculated only on the original principal
• Interest remains same every year
Formula
• Simple Interest = (P × R × T) / 100
Total Amount in SI
• Amount = P + SI
SIMPLE INTEREST – IMPORTANT OBSERVATIONS
• If time is doubled, SI is doubled
• If rate is doubled, SI is doubled
• SI is directly proportional to P, R, and T
CSAT Tip
• Use proportion logic instead of formula wherever possible
COMPOUND INTEREST (CI)
Meaning
• Interest calculated on principal plus accumulated interest
• Interest is added back to principal after each period
COMPOUND INTEREST FORMULA
For Annual Compounding
• Amount = P × (1 + R/100)ᵀ
• CI = Amount − P
For Half-Yearly Compounding
• Rate becomes R/2
• Time becomes 2T
For Quarterly Compounding
• Rate becomes R/4
• Time becomes 4T
DIFFERENCE BETWEEN SI AND CI
Key Differences
• SI is calculated only on principal
• CI is calculated on principal plus interest
• SI grows linearly
• CI grows faster over time
Important Result
• Difference between CI and SI for 2 years =
P × (R/100)²
COMPARISON LOGIC (CSAT FAVOURITE)
• For short time and low rate, SI and CI are nearly equal
• For longer duration, CI becomes much larger than SI
• Higher rate increases gap between SI and CI
WHEN CI = SI
• For one year, CI = SI
• Difference appears only after first year
INSTALLMENT AND LOAN BASED QUESTIONS
• Money paid in equal installments
• Each installment has different interest duration
• Logical distribution of interest is required
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Subject: CSAT
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