| At what rate will a sum of Rs. 1000 amount to Rs. 1102.50 in 2 yr at compound interest? [SSC (CGL) 2014] |
A) 6%
B) 6.5%
C) 5%
D) 5.5%
Correct Answer: C
Solution :
| Given, \[P=\text{Rs}.\,\,1000,\]\[T=2\,\,yr,\] |
| \[A=\text{Rs}\text{. 1102}\text{.50,}\]\[r=?\] |
| We know that, \[A=P{{\left( 1+\frac{r}{100} \right)}^{T}}\] |
| \[\Rightarrow \]\[1102.50=1000{{\left( 1+\frac{r}{100} \right)}^{2}}\] |
| \[\Rightarrow \]\[\frac{1102.50}{1000}={{\left( \frac{100+r}{100} \right)}^{2}}\]\[\Rightarrow \]\[\frac{11025}{10000}={{\left( \frac{100+r}{100} \right)}^{2}}\] |
| \[\Rightarrow \]\[{{\left( \frac{105}{100} \right)}^{2}}={{\left( \frac{100+r}{100} \right)}^{2}}\]\[\Rightarrow \]\[\frac{105}{100}=\frac{100+r}{100}\] |
| \[\Rightarrow \]\[105=100+r\]\[\Rightarrow \] \[r=105-100=5\]% |
| \[\therefore \] \[r=5\]% |
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