In what time will ₹ 5,120 amount to ₹ 7,290 at $12\dfrac{1}{2}$% per annum, compounded annually?

Given,

P = ₹ 5,120

Rate = $12\dfrac{1}{2}$% = 12.5%

A = ₹ 7,290

Let time required be n years.

$\Rightarrow A = P\Big(1 + \dfrac{r}{100}\Big)^{n } \\[1em] \Rightarrow 7290 = 5120 \times \Big(1 + \dfrac{12.5}{100}\Big)^{n} \\[1em] \Rightarrow \dfrac{7290}{5120} = \Big(\dfrac{100 + 12.5}{100}\Big)^{n} \\[1em] \Rightarrow \dfrac{729}{512} = \Big(\dfrac{112.5}{100}\Big)^{n} \\[1em] \Rightarrow \dfrac{729}{512} = \Big(\dfrac{1125}{1000}\Big)^{n} \\[1em] \Rightarrow \dfrac{729}{512} = \Big(\dfrac{9}{8}\Big)^{n} \\[1em] \Rightarrow \Big(\dfrac{9}{8}\Big)^3 = \Big(\dfrac{9}{8}\Big)^{n} \\[1em] \Rightarrow n = 3$

Hence, required time = 3 years.