A man borrows $\text{Rs. }2,550$ to be paid back with compound interest at the rate of $4\%$ per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be?

Let each equal yearly instalment be $x$.
The formula for the present value of instalments under compound interest is:

$$P=\frac{x}{1+\frac{R}{100}}+\frac{x}{{\left(1+\frac{R}{100}\right)}^2}$$

Given:
Principal ($P$) = $\text{Rs. }2,550$
Rate ($R$) = $4\%$ per annum

Calculate the factor:

$$1+\frac{R}{100}=1+\frac{4}{100}=\frac{104}{100}=\frac{26}{25}$$

Substitute into the equation:

$$2550=\frac{x}{\frac{26}{25}}+\frac{x}{{\left(\frac{26}{25}\right)}^2}$$

$$2550=\frac{25x}{26}+\frac{625x}{676}$$

Take the LCM of 26 and 676, which is 676:

$$2550=\frac{25\times 26\times x+625x}{676}$$

$$2550=\frac{650x+625x}{676}$$

$$2550=\frac{1275x}{676}$$

$$x=\frac{2550\times 676}{1275}$$

$$x=2\times 676=\text{Rs. }1352$$

Thus, each instalment will be $\text{Rs. }1,352$.