Question

In how many years ₹700 will amount to ₹847 at a compound interest rate of 10 p.c.p.a.

Answer 1

Here, P = Principal = ₹ 700
A = Amount = ₹ 847
R = 10 %
N = N years

$$\begin{gathered} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}} \\ \Rightarrow 847=700{\left(1+\frac{10}{100}\right)}^{\mathrm{N}} \\ \Rightarrow \frac{847}{700}={\left(1+\frac{1}{10}\right)}^{\mathrm{N}} \\ \Rightarrow \frac{121}{100}={\left(\frac{11}{10}\right)}^{\mathrm{N}} \\ \Rightarrow {\left(\frac{11}{10}\right)}^2={\left(\frac{11}{10}\right)}^{\mathrm{N}} \\ \Rightarrow \mathrm{N}=2 \end{gathered}$$

Hence, the number of years is 2 years.