The difference between the simple interest on a certain sum at the rate of 10\% per annum for 2 years and compound interest which is compounded every 6 months is ₹ 124.05. What is the principal sum?
(a)₹ 6000
(b)₹ 8000
(c)₹ 10,000
(d)₹ 12,000
(e)None of these
Answer
Answer (as printed): B
Explanation
Let the sum be ₹ P. Then $$\begin{aligned} & P\left[\left(1+\frac{5}{100}\right)^{4}-1\right]-\frac{P \times 10 \times 2}{100}=124.05 \\ & \Rightarrow P\left[\left(\frac{21}{20}\right)^{4}-1-\frac{1}{5}\right]=124.05 \\ & \Rightarrow P\left[\frac{194481}{160000}-\frac{6}{5}\right]=\frac{12405}{100} \\ & \Rightarrow P\left[\frac{194481-192000}{160000}\right]=\frac{12405}{100} \\ & \Rightarrow P=\left(\frac{12405}{100} \times \frac{160000}{2481}\right)=8000 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.