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

Let each yearly instalment be ₹$x$.
The rate of interest is $R=4\%$ per annum.

The formula for the present value of two equal instalments under compound interest is:

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

Given $P=2550$ and $1+\frac{R}{100}=1+\frac{4}{100}=\frac{104}{100}=\frac{26}{25}$.

Substitute these into the formula:

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

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

Find a common denominator ($676$):

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

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

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

Now, solve for $x$:

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

$$x=2\times 676=1352$$

Each instalment will be ₹$1,352$.