The sum of money which when given on compound interest at 18\% per annum would fetch ₹ 960 more when the interest is payable half yearly than when it was payable annually for 2 years is [SSC-CHSL (10+2) Exam, 2015]
(a)₹ 60,000
(b)₹ 30,000
(c)₹ 40,000
(d)₹ 50,000
Answer
Answer (as printed): D
Explanation
Rate of interest $=18 \%$ Time = 2 years When the interest is payable half yearly. Then, rate of interest $=9 \%$ per half annum. Time = 4 half years. Let the principal be ₹ $x$$$\begin{aligned} \therefore \text { C.I. } & =x\left[\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{T}}-1\right] \\ & =x\left[\left(1+\frac{9}{100}\right)^{4}-1\right] \\ & =x\left[\left(\frac{109}{100}\right)^{4}-1\right] \\ & =x[1.4116-1]=₹ 0.4116 x \end{aligned}$$ According to the question. $$\begin{aligned} & =x\left[\left(1+\frac{18}{100}\right)^{2}-1\right] \\ & =x\left[\left(\frac{118}{100}\right)^{2}-1\right] \\ & =x\left[(1.18)^{2}-1\right] \\ & =x(1.3924-1)=₹ 0.3924 x \end{aligned}$$ According to the question. $$\begin{aligned} & 0.4116 x-0.3924 x=960 \\ & \Rightarrow 0.0192 x=960 \\ & \Rightarrow x=\frac{960}{0.0192} \\ & x=\frac{960 \times 10000}{192}=₹ 50,000 \end{aligned}$$ Hence, sum of money $=₹ 50,000$
Explanation as extracted from the printed page; notation may be imperfect.