Q. A certain sum, invested at 4% per annum compound interest, compounded half yearly, amounts to 7803 Rs. at the end of one year. The sum is :
Answer: 7500 Rs.
Notes: Let the sum be P. As, the interest is compounded half-yearly, ∴ R = 2%, T = 2 half years $latex \therefore A = P \left ( 1+\frac{R}{100} \right )^{T}&s=1$ $latex => 7803 = P \left ( 1+\frac{2}{100} \right )^{2}&s=1$ $latex => 7803 = P \left ( 1+\frac{1}{50} \right )^{2}&s=1$ $latex => 7803 = P\times \frac{51}{50}\times \frac{51}{50}&s=1$ $latex => P = \frac{7803\times 50\times 50}{51\times 51} = 7500Rs&s=1$ Hence option [B] is correct answer.