Compound Interest Level 2

This module is heavy on calculation and algebraic manipulation. It requires candidates to move past basic formulas and utilize advanced shortcuts, tree methods, and effective rate percentages to solve complex multi-step word problems under time pressure.

• Target: Designed for top-tier competitive exam preparation, focusing on high-accuracy calculation and identifying the fastest solving method (formula vs. ratio vs. tree method).

• Core Syllabus & Question Types:

  • Difference Between CI and SI: A major focal point of the exam. Utilizing specific shortcut formulas for 2 and 3 years to avoid lengthy calculations:

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

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

  • Fractional Time Periods: Calculating CI when the time is not a whole number (e.g., 2 years and 73 days, or 2.5 years). Formula logic: Amount = P * (1 + R/100)^2 * (1 + (R/2)/100) for 2.5 years.

  • Compound Installments: Calculating the present value or the value of equal annual installments for a loan taken on compound interest. Formula: Loan Amount = X/(1+R/100) + X/(1+R/100)^2 + ... where X is the installment.

  • Variable Rates & Real-world Models: Problems where the interest rate changes every year (R1 for year 1, R2 for year 2), as well as population growth and machine depreciation models.