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    Subject

    Quantitative Aptitude

    Topic

    Interest

    The rate of simple interest for first 2 years is 5%, for next 2 years is 7.5% and 10% for period beyond 4 years. If the Interest after 7 years is Rs. 4400. Find the compound interest on the same principal after 2 years at 10% interest rate, compounded annually.

    ক)
    1680
    খ)
    8000
    গ)
    1980
    ঘ)
    960
    ঙ)
    1470

    Explanation

    We know that, Simple Interest = (P × R × T)/100 Where, P = principal Amount, R = % Rate of interest, T = time period in years Let the principle amount be Rs. x ∵ the interest rate is 5% per annum for first 2 years, Simple Interest for first 2 years = (x × 5 × 2)/100 = x/10 ∵ the interest rate is 7.5% per annum for next 2 years, Simple Interest for next 2 years = (x × 7.5 × 2)/100 = 3x/20 Now, the time period remaining out of total time = 7 – (2 + 2) = 3 years ∵ the interest rate is 10% per annum for remaining 3 years, Simple Interest for remaining 3 years = (x × 10 × 3)/100 = 3x/10 According to given information, total interest of 7 years = Rs. 4400 ∴ 4400 = (x/10) + (3x/20) + (3x/10) ⇒ 4400 = 11x/20 ⇒ x = (4400 × 20)/11 ⇒ x = 8000 ∴ the principal amount is Rs. 8000. We know that,  for compound interest is given by CI=P  (1+R100)T−P⇒  CI=8000×(1+10100)2−8000⇒CI=  8000×(121100−1)⇒CI=8000×21100=1680\begin{array}{l} CI = P\;{\left( {1 + \frac{R}{{100}}} \right)^T} - P\\ \Rightarrow \;CI = 8000 \times {\left( {1 + \frac{{10}}{{100}}} \right)^2} - 8000\\ \Rightarrow CI = \;8000 \times \left( {\frac{{121}}{{100}} - 1} \right)\\ \Rightarrow CI = 8000 \times \frac{{21}}{{100}} = 1680 \end{array}

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