Question: 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
Options:
A) 5%
B) 8%
C) 10%
D) 12%
Show Answer
Answer:
Correct Answer: B
Solution:
- Given, $ CI-SI=32 $ and $ P=5000 $
We know that,
$ CI=P[ {{( 1+\frac{r}{100} )}^{t}}-1 ] $
and $ SI=\frac{P\times r\times t}{100} $
According to the question,
$ P[ {{( 1+\frac{r}{100} )}^{t}}-1 ]-\frac{P\times r\times t}{100}=32 $
$ \Rightarrow $ $ 5000[ {{( 1+\frac{r}{100} )}^{2}}-1 ]-\frac{5000\times r\times 2}{100}=32 $
$ \Rightarrow $ $ 5000[ [1+\frac{r^{2}}{10000}+\frac{2r}{100}-1 ]-\frac{5000\times r\times 2}{100}=32 $
$ \Rightarrow $ $ 5000[ \frac{r^{2}}{10000}+\frac{2r}{100} ]-\frac{5000\times r\times 2}{100}=32 $
$ \Rightarrow $ $ 5000[ \frac{r^{2}+200r}{10000} ]-\frac{5000\times 2r}{100}=32 $
$ \Rightarrow $ $ \frac{5r^{2}}{10}+\frac{1000r}{10}-\frac{500\times 2r}{10}=32 $
$ \Rightarrow $ $ 5r^{2}=320 $
$ \Rightarrow $ $ r^{2}=64 $
$ \Rightarrow $ $ r=\sqrt{64} $
$ \therefore $ $ r=8 $ %
BETA
