| In what time Rs. 8000 will amount to Rs. 9261 at 10% per annum compound interest, when the interest is compounded half-yearly? |
A) \[3\frac{1}{2}yr\]
B) \[1\frac{1}{2}yr\]
C) \[2\frac{1}{2}yr\]
D) 2 yr
Correct Answer: B
Solution :
| Interest is compounded half-yearly. |
| \[\therefore \] Rate of interest = 5% |
| Time \[=\frac{n}{2}yr\](let) = n half-years |
| \[A=P{{\left( 1+\frac{r}{100} \right)}^{t}}\] |
| \[9261=8000{{\left( 1+\frac{5}{100} \right)}^{n}}\] |
| \[\Rightarrow \] \[\frac{9261}{8000}={{\left( \frac{21}{20} \right)}^{n}}\]\[\Rightarrow \]\[{{\left( \frac{21}{20} \right)}^{3}}={{\left( \frac{21}{20} \right)}^{n}}\] |
| \[\therefore \] \[n=3\] half-years \[=\frac{3}{2}yr=1\frac{1}{2}yr\] |
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