Question

The difference between the compound interest and the simple interest on a sum of money for 2 years at 10% per annum is Rs. 200. The sum is

• A. 2000
• B. 1000
• C. 20000
• D. 10000

Answer 1

The correct option is C

20000

Let P be the sum.
Compound interest = $p[{(1+\frac{x}{100})}^n-1]$, where n is the number of years and x is the interest rate.
$\Rightarrow CI=P[{(1+\frac{10}{100})}^n-1]$
$\Rightarrow CI=P({1.1}^2-1)$
$\Rightarrow CI=P(1.21-1)=0.21P$
Simple interest $P\times n\times \frac{x}{100}=P\times 2\times \frac{10}{100}=0.2P$
Given, Difference between compound interest and simple interest is Rs.200
$\Rightarrow$ 0.21P - 0.2P = 200
$\Rightarrow$ 0.01P = 200 $\Rightarrow$ P = $\frac{200}{0.01}$ = Rs. 20000