| A sum of money becomes eight times in 3 yr, if the rate is compounded annually. In how much time will the same amount at the same compound rate become sixteen times? [SSC (CGL) 2011] |
A) 6 yr
B) 4 yr
C) 8 yr
D) 5 yr
Correct Answer: B
Solution :
| Let the principal be Rs. 1. |
| Then, amount is Rs. 8. |
| Now, \[A=P{{\left( 1+\frac{r}{100} \right)}^{T}}\] |
| \[\Rightarrow \]\[8=1{{\left( 1+\frac{r}{100} \right)}^{3}}\] |
| \[\Rightarrow \] \[{{2}^{3}}={{\left( 1+\frac{r}{100} \right)}^{3}}\]\[\Rightarrow \]\[2={{\left( 1+\frac{r}{100} \right)}^{1}}\] |
| On squaring twice both sides, we get |
| \[{{2}^{4}}={{\left( 1+\frac{r}{100} \right)}^{4}}\] |
| \[\therefore \] \[16={{\left( 1+\frac{r}{100} \right)}^{4}}\] |
| So, in 4 yr the same amount at the same compound rate become sixteen times |
| \[\therefore \] Time = 4 yr |
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