Question

The compound interest on a certain sum of money for 2 years at 10$\%$ per annum is Rs 420. Find the simple interest on the same sum at the same rate and for the same time.

• A. $Rs.380$
• B. $Rs.400$
• C. $Rs.350$
• D. $Rs.375$

Answer 1

Answer: (B)

Given that, the compound interest on certain sum of money for $2$ years at $10\%$ per annum is $Rs.420$

To find out: The simple interest on the same amount at the same rate and for the same time.

Let the principal amount be $Rs.x$

We know that, $CI=P[{(1+\frac{R}{100})}^T-1]$

Here, $CI=Rs.420,R=10\%andT=2$

$\therefore 420=x[{(1+\frac{10}{100})}^2-1]$

$\Rightarrow 420=x[{\left(\frac{11}{10}\right)}^2-1]$

$\Rightarrow 420=x[\left(\frac{121}{100}\right)-1]$

$\Rightarrow 420=x\left(\frac{121-100}{100}\right)$

$\Rightarrow x=\frac{420\times 100}{21}$

$\therefore x=Rs.2000$

Now, we also know that,

$SI=\frac{P\times R\times T}{100}$

Here, $P=Rs.2000,R=10\%andT=2$

$\therefore SI=\frac{2000\times 10\times 2}{100}$

$\Rightarrow SI=\frac{40000}{100}$

$\therefore SI=Rs.400$

Hence, the simple interest on the same amount, at the same rate of interest and for the same time is $Rs.400$.