Quantitative Aptitude
Number System Percentage Profit, Loss & Discount Time & Work Speed, Distance & Time Simple & Compound Interest Ratio, Proportion & Mixture Mensuration Data Interpretation
Module 2 · IBPS PO Quantitative Aptitude

Simple & Compound Interest

SI, CI, installment problems, interest rate comparisons.
Simple Interest · Compound Interest · Installments
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Learning Objectives

  • Understand the fundamental concepts of Simple & Compound Interest
  • Apply key formulas and techniques to solve problems
  • Practice with exam-level questions to build speed and accuracy

Key Concepts

What is Simple & Compound Interest?

Interest is the cost of borrowing money. Simple interest is calculated on the principal amount only, while compound interest is calculated on the principal and accumulated interest. Both are frequently tested in SSC CGL Tier 1.

Key Concepts

1. Simple Interest (SI): SI = (P * R * T) / 100, where P = Principal, R = Rate% per annum, T = Time in years. Amount = P + SI.

2. Compound Interest (CI): Amount = P * (1 + R/100)^T. CI = Amount - P. For half-yearly compounding: Amount = P * (1 + R/200)^(2T). For quarterly: Amount = P * (1 + R/400)^(4T).

3. CI vs SI for 2 years: CI - SI = P * (R/100)^2. For 3 years: CI - SI = P * (R/100)^2 * (300 + R)/100.

4. Installments: Each installment includes principal repayment and interest on the outstanding principal. The formula for equal annual installments is best approached using PV = Installment / (1 + r)^n logic.

Solved Examples

Example 1 (Simple Interest)
Find the simple interest on Rs.5000 at 8% per annum for 3 years.

a) Rs.1000 b) Rs.1100 c) Rs.1200 d) Rs.1300
Solution: c) Rs.1200. SI = (5000 * 8 * 3)/100 = 1200.
Example 2 (Compound Interest)
Find the compound interest on Rs.10000 at 10% p.a. for 2 years.

a) Rs.2000 b) Rs.2100 c) Rs.2200 d) Rs.2300
Solution: b) Rs.2100. Amount = 10000 * (1 + 10/100)^2 = 10000 * 1.21 = 12100. CI = 12100 - 10000 = 2100.
Example 3 (CI - SI Difference)
The difference between CI and SI on a sum for 2 years at 5% p.a. is Rs.25. Find the principal.

a) Rs.8000 b) Rs.10000 c) Rs.12000 d) Rs.15000
Solution: b) Rs.10000. CI - SI = P * (R/100)^2. 25 = P * (5/100)^2 = P * 1/400. P = 25 * 400 = 10000.

Shortcut Techniques

  • For SI, use fractions: 10% per annum = 1/10 of principal per year. For T years at R%, SI = P * R * T / 100.
  • For CI, when rate is 5%, multiply by 21/20 for each year. For 10%, multiply by 11/10.
  • For CI with two years, (1 + R/100)^2 = 1 + 2R/100 + (R/100)^2. The (R/100)^2 term is the extra over SI.
  • For finding rate when CI - SI is given for 2 years: R = 100 * sqrt((CI-SI)/P).
Pro Tip: In SSC CGL, CI questions often use "yearly, half-yearly, or quarterly" compounding. Adjust R and T accordingly. For the difference between CI and SI, use the direct formula rather than calculating both separately.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Practice Questions

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