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A certain sum, invested at 4% per annum compound interest, compounded half yearly, amounts to Rs. 7803 at the end of one year. The sum is ?

a) Rs. 7000
b) Rs. 7200
c) Rs. 7500
d) Rs. 7700

Answer: c
Explanation: Time (t) = 1 years
Rate % = 4%
Amount = Rs. 7803
When interest is compounded half yearly
New Rate = $$\frac{4}{2}$$ = 2%
Time = 1 × 2 = 2 years
Required rate% for 2 years CI
$${\text{ = 2}} + {\text{2}} + \frac{{2 \times 2}}{{100}} = 4.04\% $$
(100 + 4.04)% of sum = Rs. 7803
$$\eqalign{ & {\text{Sum = }}\frac{{7803}}{{104.04}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}7500 \cr} $$

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