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The simple interest on a sum of money at 4% per annum for 2 years is Rs 80. The compound interest on the same sum for the same period is = ?

a) Rs. 82.60
b) Rs. 82.20
c) Rs. 81.80
d) Rs. 81.60

Answer: d
Explanation:
$$\eqalign{ & {\text{Rate }}\% {\text{ = 4}}\% \cr & {\text{Time (}}{{\text{t}}_1}) = 2\,{\text{years}} \cr & {\text{SI for 2 years}} \cr & {\text{ = 4}} \times {\text{2 = 8}}\% \cr & {\text{CI for 2 years}} \cr & {\text{ = 4 + 4 + }}\frac{{4 \times 4}}{{100}} \cr & = 8.16\% \cr & \operatorname{Required} \,CI = \frac{{80}}{8} \times 8.16 \cr & = Rs.\,81.60 \cr} $$

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