Question

The difference between simple and compound interest on sum of $10000$ is $64$ for $2$ years. Find the rate of interest.

• A. $8$
• B. $64$
• C. $4$
• D. $2$

Answer 1

The correct option is A $8$

Simple Interest $=\frac{PNR}{100}$

Compound Interest $=P{(1+\frac{R}{100})}^N-P$

Now,

$P{(1+\frac{R}{100})}^N-P$ $-\frac{PNR}{100}=64$

$[10000\times {(1+\frac{R}{100})}^2-10000]-\left(\frac{10000\times R\times 2}{100}\right)=64$

$\Rightarrow$ $10000[{(1+\frac{R}{100})}^2-1-\frac{2R}{100}]=64$

$\Rightarrow$ $10000[\frac{(100+R{)}^2}{10000}-1-\frac{2R}{100}]=64$

$\Rightarrow$ $10000\left[\frac{10000+200R+R^2-10000-200R}{10000}\right]=64$

$\Rightarrow$ $R^2=64$

$\Rightarrow$ $R=8$

$\therefore$ $Rate=8\%$