A) \[1\frac{1}{2}\]yr
B) 2 yr
C) 1 yr
D) \[2\frac{1}{2}\]yr
Correct Answer: A
Solution :
| Let the required lime = t years |
| Interest is compounded half yearly. |
| \[\therefore \]Time = 2t half years and rate \[=\frac{20}{2}=10%\] |
| \[\therefore \] \[1000{{\left( 1+\frac{10}{100} \right)}^{2t}}=1331\] |
| \[\Rightarrow \] \[{{\left( \frac{11}{10} \right)}^{2t}}=\frac{1331}{1000}\] |
| \[\Rightarrow \] \[{{\left( \frac{11}{10} \right)}^{2t}}={{\left( \frac{11}{10} \right)}^{3}}\] |
| \[\Rightarrow \] \[2t=3\] |
| \[\therefore \] \[t=\frac{3}{2}\text{yr}\] |
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