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    Question

    A sum of money earns Rs.500 as Simple Interest (SI) in

    2 years at r% per annum. If the Compound Interest (CI) compounded annually for 2 years is Rs.25 more than the SI, find he Amount after 2 years at CI
    A Rs.2200 Correct Answer Incorrect Answer
    B Rs.2300 Correct Answer Incorrect Answer
    C Rs.3025 Correct Answer Incorrect Answer
    D Rs.7300 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Given: SI (2 years) = 500 CI − SI (2 years) = 25 Formulas: SI for 2 years = (P * r * 2) / 100 For 2 years (compounded annually): CI − SI = P * (r/100)^2 Use SI equation (P * r * 2) / 100 = 500 P * r = 500 * 100 / 2 = 25000 ...(1) Use (CI − SI) equation P * (r/100)^2 = 25 P * r^2 / 10000 = 25 P * r^2 = 25 * 10000 = 250000 ...(2) Step 3: Divide (2) by (1) (P * r^2) / (P * r) = 250000 / 25000 r = 10 Find P from (1) P * 10 = 25000 P = 2500 Amount after 2 years at CI A = P * (1 + r/100)^2 A = 2500 * (1.10)^2 = 2500 * 1.21 = 3025 Amount after 2 years (CI) = Rs.3025

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