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: Option C
Solution(By Examveda Team)
Time (t) = 1 yearsRate % = 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
$${\text{ = 2}} + {\text{2}} + \frac{{2 \times 2}}{{100}} = 4.04\% $$
According to question,
(100 + 4.04)% of sum = Rs. 7803
$$\eqalign{ & \therefore {\text{Sum = }}\frac{{7803}}{{104.04}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}7500 \cr} $$
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