Find the respective ratio of the simple interest and the compound interest on ₹100 at 10% per annum for 2 years. when compound interest is compounded annually.

Ratio of simple and compound interest = $$\frac{principal\times\ rate\times\ time}{100}$$ : $$principal\left[\left(1+\frac{rate}{100}\right)^{time}-1\right]$$

= $$\frac{100\times10\times2}{100}\ :\ 100\left[\left(1+\frac{10}{100}\right)^2-1\right]$$

= $$10\times2\ :\ 100\left[\left(1+\frac{1}{10}\right)^2-1\right]$$

= $$20\ :\ 100\left[\left(\frac{11}{10}\right)^2-1\right]$$

= $$20\ :\ 100\left[\frac{121}{100}-1\right]$$

= $$20\ :\ 100\times\frac{21}{100}$$

= 20 : 21