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Compound Interest compounded quarterly on Rs. 15000 for 3 years is Rs. 986 more than Simple Interest on the same principal for 3 years. Find the rate of interest. |
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Answer» Step-by-step explanation: Quarterly interest paying for 3 years means 4 * 3 = 12 interest paying terms. Let the RATE of interest per year = r % So, quarterly interest = (r/100) * (3/12) = r/400 Simple interest for 3 years = 15000 * (r/400) * 12 = 450r COMPOUND interest for 3 years = 15000 * (1 + r/400)^12 - 15000 Since, compound interest = simple interest + 986 So, 15000 * (1 + r/400)^12 - 15000 = 450r + 986 Rearranging, 15000 * (1 + r/400)^12 - 450r = 986 + 15000 = 15986 Or, dividing both sides by 15000, we get, (1 + r/400)^12 = 450r/15000 + 15986/15000 Or, (1 + r/400)^12 = 0.03r + 1.0657 Or (1 + r/400)^12 - 0.03r = 1.0657 This is an equation, that requires trial & error METHOD to solve. Assume r = 5%, LHS = (1 + 5/400)^12 - 0.03 * 5 = 1.011 Next assume r = 10% LHS = (1 + 10/400)^12 - 0.03 * 10 = 1.0449 Next assume r = 12%, LHS = (1 + 12/400)^12 - 0.03 * 12 = 1.0657 So, rate of interest = 12 % Ans. 738 viewsView 2 Upvoters Related Questions (More Answers Below) |
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