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A sum of Rs. 8000 will amount to Rs. 8820 in 2 years if the interest is calculated every year. The rate of compound interest is = ?

a) 6%
b) 7%
c) 3%
d) 5%

Answer: d
Explanation:
$$\eqalign{ & {\text{Principal = Rs 8000}} \cr & {\text{Amount = Rs 8820}} \cr & {\text{Let Rate = }}R \cr & {\text{Time = 2 years}} \cr & {\text{By using formula, }} \cr & 8820 = 8000{\left( {1 + \frac{R}{{100}}} \right)^2} \cr & \frac{{8820}}{{8000}} = {\left( {1 + \frac{R}{{100}}} \right)^2} \cr & \frac{{441}}{{400}} = {\left( {1 + \frac{R}{{100}}} \right)^2} \cr & {\text{Taking square root of both sides,}} \cr & \frac{{21}}{{20}} = \left( {1 + \frac{R}{{100}}} \right) \cr & R = 5\% \cr} $$

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