Simple & Compound Interest: Concepts

Idea: Calculating principal amounts when the difference between Compound and Simple Interest over 2 or 3 years is provided.
Equation: For 2 years: $CI-SI = P(r/100)^2$ . For 3 years: $CI-SI = P(r/100)^2(3+r/100)$ .
Example: Find the difference between CI and SI on ₹8000 at 10% for 2 years. Solution: Difference $= 8000\times(10/100)^2 = 8000\times0.01 = ₹80$ .

Idea: Parallel evaluation of investment growth under simple versus compound rules.
Equation: $SI = \frac{P\times R\times T}{100},\quad A = P\left(1+\frac{R}{100}\right)^T$
Example: At what rate does a sum double in 8 years at simple interest? Solution: $P\times R\times8/100 = P \Rightarrow R = 100/8 = 12.5\%$ .

Idea: Applying compound interest formulas to municipal growth and machinery devaluation.
Equation: Growth: $P_n = P_0(1+r/100)^n$ . Depreciation: $V_n = V_0(1-r/100)^n$ .
Example: A machine worth ₹50,000 depreciates 10% annually. Find its value after 3 years. Solution: $V = 50000(0.9)^3 = 50000\times0.729 = ₹36,450$ .

SI & CI Concepts