Compound Interest (Using Formula)

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A = P(1 + r/100)ⁿ Where: A = Amount P = Principal r = Rate of interest per annum n = Number of years This formula helps us calculate the total amount after compound interest without finding CI separ

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C.I. = P[(1 + r/100)ⁿ - 1] Or alternatively: C.I. = A - P The first formula directly gives compound interest without calculating amount first. The second requires finding amount first and then subtr

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Given: P = ₹5,000, n = 2 years, r = 8% Using A = P(1 + r/100)ⁿ A = ₹5,000(1 + 8/100)² A = ₹5,000(1.08)² A = ₹5,000 × 1.1664 A = ₹5,832 Therefore, Amount = ₹5,832

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A = P(1 + r₁/100)(1 + r₂/100)(1 + r₃/100)... Where: r₁%, r₂%, r₃%... are rates for 1st, 2nd, 3rd year respectively Example: For 3 years with rates 10%, 12%, 15%: A = P(1 + 10/100)(1 + 12/100)(1 + 15

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From A = P(1 + r/100)ⁿ We get: P = A / (1 + r/100)ⁿ Example: If A = ₹6,050, r = 10%, n = 2 years P = ₹6,050 / (1 + 10/100)² P = ₹6,050 / (1.1)² P = ₹6,050 / 1.21 P = ₹5,000

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From A = P(1 + r/100)ⁿ We get: (1 + r/100) = (A/P)^(1/n) Therefore: r = 100[(A/P)^(1/n) - 1] Example: If P = ₹8,000, A = ₹9,680, n = 2 years (1 + r/100) = (9,680/8,000)^(1/2) = (1.21)^(1/2) = 1.1 S

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From A = P(1 + r/100)ⁿ We get: (1 + r/100)ⁿ = A/P Solve by comparing both sides to find n. Example: If P = ₹4,000, A = ₹4,840, r = 10% (1.1)ⁿ = 4,840/4,000 = 1.21 = (1.1)² Therefore, n = 2 years

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For 2 years: C.I. - S.I. = P × r² / (100)² This formula is very useful for solving problems where the difference between CI and SI is given. Example: If difference is ₹25 and rate is 5% 25 = P × (5)