Question

Tick (✓) the correct answer:
At what rate per cent per annum will a sum of Rs 7500 amount to Rs 8427 in 2 years, compounded annually?
(a) 4%
(b) 5%
(c) 6%
(d) 8%

Answer 1

(c) 6%

$$\begin{gathered} \mathrm{Here},A=P\times \left(1+\frac{R}{100}\right) \\ =\mathrm{Rs}.7500\times {\left(1+\frac{R}{100}\right)}^2 \\ =\mathrm{Rs}.7500\times {\left(1+\frac{R}{100}\right)}^2 \\ \mathrm{However},\mathrm{amount}=\mathrm{Rs}.8427 \\ \mathrm{Now},\mathrm{Rs}.8427==\mathrm{Rs}.7500\times {\left(1+\frac{R}{100}\right)}^2 \\ \Rightarrow \frac{\mathrm{Rs}.8427}{\mathrm{Rs}.7500}={\left(1+\frac{R}{100}\right)}^2 \\ \Rightarrow {\left(\frac{53}{50}\right)}^2={\left(1+\frac{R}{100}\right)}^2 \\ \Rightarrow \left(1+\frac{R}{100}\right)=\left(\frac{53}{50}\right) \\ \Rightarrow \frac{R}{100}=\frac{53}{50}-1 \\ \Rightarrow \frac{R}{100}=\frac{53-50}{50}=\frac{3}{50} \\ \therefore R=\frac{300}{50}=6\% \end{gathered}$$