Q19
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
AnswerC.
16 years
D.
24 years
Answer: Option B
Solution
Answer: Option B
Solution:
\begin{aligned}
& {\text{Let Principal = P}} \\
& {\text{Rate = R% }} \\
& {\text{T = 4 years}} \\
& \therefore {\text{Amount = 2P}} \\
& {\text{Case (I) 2P = P}}{\left( {1 + \frac{R}{{100}}} \right)^4} \\
& 2 = {\left( {1 + \frac{R}{{100}}} \right)^4}.....(i) \\
& {\text{Case (II) Let after t years it will be 8 times}} \\
& {\text{8P = P}}{\left( {1 + \frac{R}{{100}}} \right)^t} \\
& {\left( 2 \right)^3} = {\left( {1 + \frac{R}{{100}}} \right)^t}.....(ii) \\
& {\text{By using equation (i) & equation (ii)}} \\
& {\left( {1 + \frac{R}{{100}}} \right)^{12}} = {\left( {1 + \frac{R}{{100}}} \right)^t} \\
& {\text{By comparing both sides,}} \\
& {\text{t = 12 years}} \\\end{aligned}