A sum of money is paid back in two annual instalments of $\text{₹ }1,764$ each, allowing $5\%$ compound interest compounded annually. The sum borrowed was:

Let the sum borrowed (present value) be $P$.
* Annual instalment amount, $X=\text{₹ }1,764$
* Rate of interest, $r=5\%=0.05$ per annum
* Number of instalments, $n=2$

The formula relating the principal with its compound interest instalments is:

$$P=\frac{X}{1+r}+\frac{X}{(1+r{)}^2}$$

Substitute the given values into the formula:

$$P=\frac{1764}{1+0.05}+\frac{1764}{(1+0.05{)}^2}$$

$$P=\frac{1764}{1.05}+\frac{1764}{(1.05{)}^2}$$

Let's compute each term:

$$\text{First term}=\frac{1764}{1.05}=1680$$

$$\text{Second term}=\frac{1764}{1.1025}=1600$$

Summing them up gives the total principal borrowed:

$$P=1680+1600=\text{₹ }3,280$$