In how may years will a sum of $$₹ 320$$ amount to $$₹ 405$$ if interest is compounded at 12.5% per annum?

Given,

Principal (P) = $$₹ 320$$

Rate (R)% = 12.5%

Amount (A) = $$₹ 405$$

Let the required number of years = n

$$=$$>  $$\text{P}\left(1+\frac{\text{R}}{100}\right)^n=405$$

$$=$$>  $$320\left(1+\frac{12.5}{100}\right)^n=405$$

$$=$$>  $$320\left(\frac{112.5}{100}\right)^n=405$$

$$=$$>  $$\left(\frac{1125}{1000}\right)^n=\frac{405}{320}$$

$$=$$>  $$\left(\frac{9}{8}\right)^n=\frac{81}{64}$$

$$=$$>  $$\left(\frac{9}{8}\right)^n=\frac{9^2}{8^2}$$

$$=$$>  $$\left(\frac{9}{8}\right)^n=\left(\frac{9}{8}\right)^2$$

$$=$$>  $$n=2$$

Hence, the correct answer is Option A