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Simple & Compound Interest Notes

Questions

2 questions per paper

Difficulty

Medium

Importance

High yield for SSC and Banking

Overview

Simple and Compound Interest form the backbone of Quantitative Aptitude in competitive exams like SSC and Banking. Mastering these concepts is essential because they frequently appear in data interpretation and arithmetic sections, requiring both conceptual clarity and speed-solving tricks to manage strict time constraints.

Simple Interest (SI) Basics

Simple interest is calculated exclusively on the original principal amount for the entire duration of the loan. It follows a linear progression, making it straightforward to calculate mentally if the rate and time are integers.

  • SI = (P * R * T) / 100
  • Amount (A) = P + SI
  • Simple Interest remains constant for every year
  • P = (100 * SI) / (R * T)

Compound Interest (CI) Fundamentals

Compound interest is interest calculated on the principal plus any previously accumulated interest, leading to exponential growth. For exams, using the effective rate method is significantly faster than the traditional formula.

  • A = P * (1 + R/100)^n
  • CI = P * [(1 + R/100)^n - 1]
  • Effective Rate for 2 years = 2R + (R^2/100)%
  • For half-yearly, R becomes R/2 and T becomes 2T
  • For quarterly, R becomes R/4 and T becomes 4T

Difference Between SI and CI

The difference between SI and CI arises because CI charges interest on interest. Questions on this topic are very common in prelims and can be solved instantly using specific shortcut formulas for 2 and 3-year durations.

  • Diff for 2 years = P * (R/100)^2
  • Diff for 3 years = P * (R/100)^2 * [(R/100) + 3]
  • Ratio of CI/SI for 2 years = (200 + R) / 200
  • Always remember: CI > SI for any period greater than 1 year

Installments and Annuities

Installment problems involve repaying a debt in fixed periodic payments. While these can be algebraically intensive, using the reverse-calculation or 'equal principal' method helps in finding the yearly installment value quickly.

  • SI Installment = [100 * Amount] / [100 * T + (R * T * (T-1))/2]
  • CI Installment (2 equal payments) = P = X/(1+R/100) + X/(1+R/100)^2
  • For CI installments, treat each installment as a backward-discounted value
  • Always visualize the cash flow to avoid setup errors

Formula Sheet

SI = (P*R*T)/100

CI = P * [(1 + R/100)^n - 1]

Difference (2 years) = P * (R/100)^2

Difference (3 years) = P * (R/100)^2 * (R/100 + 3)

Effective Rate (2 years) = 2R + R^2/100

Amount = P(1 + R/100)^n

Exam Tip

Instead of using the heavy CI formula, memorize the effective percentage rates for common rates (like 5%, 10%, 20%) to solve 2-year CI problems in seconds.

Common Mistakes

  • Confusing simple interest with compound interest formulas during high-pressure sections.
  • Forgetting to adjust the rate (R) and time (T) when the compounding frequency changes from annual to half-yearly or quarterly.
  • Attempting long-form calculations instead of using the effective percentage increase method for CI.

More Revision Notes

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