Question

On what sum of money will the difference between the simple interest and the compound interest for $3$ years at $8\%$ annum be equal to Rs. $100$?

• A. $10000$
• B. $20000$
• C. $30000$
• D. $40000$

Answer 1

The correct option is A $10000$

Compound interest $=A-P$
CI $=P{(1+\frac{R}{100})}^n-P$

$=P{[1+\frac{8}{100}]}^3-1]$
$=0.25P$
Simple interest, SI $=$ $\frac{PNR}{100}$
SI $=\frac{P\times 8\times 3}{100}$
SI $=0.24P$
Now, it is given that CI $-$ SI $=100$
$\Rightarrow 0.25P-0.24P=100$
$\Rightarrow P=\frac{100}{0.01}$
$\Rightarrow P=$ Rs. $10000$