A sum of money doubles itself in 4 years compound interest. It will amount to 8 times itself at the same rate of interest in = ?
A. 18 years
B. 12 years
C. 16 years
D. 24 years
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let Principal = P}} \cr & {\text{Rate = R% }} \cr & {\text{T = 4 years}} \cr & \therefore {\text{Amount = 2P}} \cr & {\text{Case (I) 2P = P}}{\left( {1 + \frac{R}{{100}}} \right)^4} \cr & 2 = {\left( {1 + \frac{R}{{100}}} \right)^4}.....(i) \cr & {\text{Case (II) Let after t years it will be 8 times}} \cr & {\text{8P = P}}{\left( {1 + \frac{R}{{100}}} \right)^t} \cr & {\left( 2 \right)^3} = {\left( {1 + \frac{R}{{100}}} \right)^t}.....(ii) \cr & {\text{By using equation (i) & equation (ii)}} \cr & {\left( {1 + \frac{R}{{100}}} \right)^{12}} = {\left( {1 + \frac{R}{{100}}} \right)^t} \cr & {\text{By comparing both sides,}} \cr & {\text{t = 12 years}} \cr} $$Related Questions on Compound Interest
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B. Rs. 121
C. Rs. 122
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E. None of these
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B. 630
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D. 650
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