Difference between CI and SI on Rs. $5{,}000$ at $10\%$ p.a. for $2$ years (compounded annually) is

Difference between CI and SI on Rs. $5{,}000$ at $10\%$ p.a. for $2$ years (compounded annually) is
  1. Rs. $40$
  2. Rs. $50$
  3. Rs. $55$
  4. Rs. $60$

Solution

Shortcut for $2$ years: $\text{CI} - \text{SI} = P \left(\dfrac{R}{100}\right)^{2} = 5000 \times \dfrac{1}{100} = 50$. Check: SI $= \dfrac{5000 \cdot 10 \cdot 2}{100} = 1000$, CI $= 1050$, difference $= 50$.

Asked in: IMO

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