Question
A sum of money amounts to Rs 2420 in 2 years and Rs 2662
in 3 years at compound interest. Find the rate of interest per annum and the principal.Solution
Let principal = P, rate = r% per annum. Amount after 2 years: A₂ = P(1 + r)² = 2420 Amount after 3 years: A₃ = P(1 + r)³ = 2662 Divide A₃ by A₂: A₃/A₂ = (1 + r)³ / (1 + r)² = 1 + r So 2662/2420 = 1 + r Check ratio: 2420 × 1.1 = 2662 ⇒ 2662/2420 = 1.1 Thus 1 + r = 1.1 ⇒ r = 0.1 = 10% Now P(1.1)² = 2420 P(1.21) = 2420 ⇒ P = 2420 / 1.21 = 2000 Rate = 10% p.a., Principal = Rs 2000.
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