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 ?

Answer: Option C

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
$$\text{ = 2}+\text{2}+\frac{2\times 2}{100}=4.04\%$$
According to question,
(100 + 4.04)% of sum = Rs. 7803
$$\begin{array}{rl}& \therefore \text{Sum = }\frac{7803}{104.04}\times 100\\ & =\text{Rs}\text{. }7500\end{array}$$