| The difference between the compound interest and simple interest for the amount Rs. 5000 in 2 yr is Rs. 32. The rate of interest is [SSC (CGL) 2011] |
A) 5%
B) 8%
C) 10%
D) 12%
Correct Answer: B
Solution :
| Given, \[CI-SI=32\] and \[P=5000\] |
| We know that, |
| \[CI=P\left[ {{\left( 1+\frac{r}{100} \right)}^{t}}-1 \right]\] |
| and \[SI=\frac{P\times r\times t}{100}\] |
| According to the question, |
| \[P\left[ {{\left( 1+\frac{r}{100} \right)}^{t}}-1 \right]-\frac{P\times r\times t}{100}=32\] |
| \[\Rightarrow \]\[5000\left[ {{\left( 1+\frac{r}{100} \right)}^{2}}-1 \right]-\frac{5000\times r\times 2}{100}=32\] |
| \[\Rightarrow \]\[5000\left[ [1+\frac{{{r}^{2}}}{10000}+\frac{2r}{100}-1 \right]-\frac{5000\times r\times 2}{100}=32\] |
| \[\Rightarrow \]\[5000\left[ \frac{{{r}^{2}}}{10000}+\frac{2r}{100} \right]-\frac{5000\times r\times 2}{100}=32\] |
| \[\Rightarrow \] \[5000\left[ \frac{{{r}^{2}}+200r}{10000} \right]-\frac{5000\times 2r}{100}=32\] |
| \[\Rightarrow \] \[\frac{5{{r}^{2}}}{10}+\frac{1000r}{10}-\frac{500\times 2r}{10}=32\] |
| \[\Rightarrow \] \[5{{r}^{2}}=320\]\[\Rightarrow \]\[{{r}^{2}}=64\]\[\Rightarrow \]\[r=\sqrt{64}\] |
| \[\therefore \] \[r=8\]% |
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