The difference between compound and simple interests on a certain sum of money at the interest rate of 10% per annum for $1\frac{1}{2}$ years is ₹183, when the interest is compounded semi-annually. Find the sum of money. (S.S.C., 2007)
Answer
Answer (as printed):
Explanation
Let the sum be ₹x. Then, C.I. $=₹\left[x\left(1+\frac{5}{100}\right)^{3}-x\right]=₹\left[\left(x \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20}\right)-x\right]=₹\left(\frac{9261x}{8000}-x\right)=₹\left(\frac{1261x}{8000}\right)$. S.I. $=₹\left(\frac{x \times 10 \times 3}{100 \times 2}\right)=₹\frac{3x}{20}$. ∴ $\frac{1261x}{8000}-\frac{3x}{20}=183 \Rightarrow \frac{61x}{8000}=183$ $\Rightarrow x=\left(\frac{183 \times 8000}{61}\right)=24000$. Hence, required sum $=₹24000$.
Explanation as extracted from the printed page; notation may be imperfect.