Question
An amount of Rs. 'x' is invested
at a simple interest rate of 15% per annum and grows to Rs. 14,500 after 3 years. If the same amount Rs. 'x' is instead invested at a compound interest rate of 20% per annum, compounded semi-annually, it becomes Rs. 13,310 after an unknown period. Determine the time required for this compound interest investment.Solution
ATQ, {x + (x × 15 × 3)/100} = 14500 Or, 1.45x = 14500 Or, x = 10000 According to the question, When Rs. 'x' is invested at compound interest, Effective rate of interest = (20/2) = 10% Assume the desired time period be ‘2a’ half years. So, 13310 = 10000 × {1 + (10/100)}2a Or, (1331/1000) = (11/10)2a Or, (11/10)3 = (11/10)2a Or, 2a = 3 Or, a = (3/2) years
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