Question
If the difference between the simple interest and
compound interest, compounded annually, received on a principal amount of Rs. 25000 at an interest rate of (a + 2)% for 2 years is Rs. 160, calculate the time required for an investment at a simple interest rate of (a + 4)% per annum to double.Solution
ATQ, Difference between the compound interest and simple interest received for 2 years = P(R/100)2 where P = sum invested, R = rate of interest According to the question, 25000 × {(a + 2)2/10000} = 160 Or, (a + 2)2 = 1600000/25000 = 64 Or, a + 2 = 8 (Since, rate cannot be negative) Or, a = 6 Let, time required to double a certain sum i.e. Rs. 's' = t years Rate of interest = (a + 4) = 10% p.a. So, {(s × 10 × t)/100} = 2s – s = s Or, 10t = 100 Or, t = 10 Required time = 10 years
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