InterviewSolution
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A sum of money becomes eight times in 3 years, if the rate is compounded annually. In how much time will the same amount at the same compound rate become sixteen times ?1). 6 years2). 4 years3). 8 years4). 5 years |
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Answer» Formula for compound INTEREST:- $(A = P{\left( {1 + \FRAC{R}{{100}}} \right)^T})$, CI = A – P Where CI is compound interest, A is amount, P is principal, R is rate, T is time Given, Sum of money BECOMES 8 times in 3 years. ∴ A = 8P $(\Rightarrow 8{\rm{P}} = P{\left( {1 + \frac{R}{{100}}} \right)^3})$ $(\Rightarrow {\rm{\;}}8 = {\left( {1 + \frac{R}{{100}}} \right)^3})$ $(\Rightarrow {2^3} = {\left( {1 + \frac{R}{{100}}} \right)^3})$ ⇒ 2 = 1 + R/100 ⇒ R = 100 % Let the time be T in which sum of money becomes 16 times of itself. ∴ A = 16P $(\Rightarrow 16{\rm{P\;}} = P{\left( {1 + \frac{R}{{100}}} \right)^T})$ $(\Rightarrow 16{\rm{\;}} = {\left( {1 + \frac{{100}}{{100}}} \right)^T})$ ⇒ 24 = 2T By property of indices ; ab = ac, ⇒ b = c ⇒ T = 4 years |
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