# 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

A. Rs. 120

B. Rs. 121

C. Rs. 122

D. Rs. 123

E. None of these

A. 625

B. 630

C. 640

D. 650

E. None of these

A. Rs. 2160

B. Rs. 3120

C. Rs. 3972

D. Rs. 6240

E. None of these

A. Rs. 2.04

B. Rs. 3.06

C. Rs. 4.80

D. Rs. 8.30

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