A doctor borrowed $\text{₹}3,825$ and he returned the money in two equal yearly instalments. If the annual rate of compound interest (compounded annually) is $4\%$, then find the value of each instalment.

Let each equal yearly instalment be $x$.
The rate of interest is $R=4\%$ per annum.
The present value of the instalments must equal the borrowed amount:

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

Given $\text{Principal}=3825$ and $1+\frac{4}{100}=\frac{104}{100}=\frac{26}{25}$:

$$3825=\frac{x}{\left(\frac{26}{25}\right)}+\frac{x}{{\left(\frac{26}{25}\right)}^2}$$

$$3825=\frac{25x}{26}+\frac{625x}{676}$$

Taking the common denominator as $676$:

$$3825=\frac{25\times 26\times x+625x}{676}$$

$$3825=\frac{650x+625x}{676}$$

$$3825=\frac{1275x}{676}$$

$$x=\frac{3825\times 676}{1275}$$

Since $1275\times 3=3825$:

$$x=3\times 676=2028$$

Thus, the value of each instalment is $\text{₹}2,028$.