A sum of money placed at compound interest double itself in 4 years. In how many years will it amount to four times itself ?
A. 12 years
B. 13 years
C. 8 years
D. 16 years
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let}}, \cr & {\text{Principal}} = Rs.\,100\% \cr & {\text{Amount}} = Rs.\,200 \cr & {\text{Rate}} = r\% \cr & {\text{Time}} = 4\,{\text{years}} \cr & {\text{Now}}, \cr & A = P \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^n} \cr & 200 = 100 \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} \cr & 2 = {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} - - - - - - \left( i \right) \cr & {\text{If}}\,{\text{sum}}\,{\text{become}}\,{\text{8}}\,{\text{times}}\,{\text{in}}\,{\text{the}}\,{\text{time}}\,n\,{\text{years}} \cr & {\text{then,}} \cr & 4 = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {2^2} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} - - - - - - \left( {ii} \right) \cr & {\text{Using}}\,{\text{eqn}}\,\left( i \right)in\left( {ii} \right),\,{\text{we}}\,{\text{get}} \cr & {\left( {{{\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]}^4}} \right)^2} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^{8}} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {\text{Thus}},\,n = 8\,{\text{years}}. \cr} $$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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