A certain sum, at a certain rate of simple interest, amounts to ₹$2,225$ in $4$ years and ₹$2,606$ in $8$ years. Find the amount (in ₹) of the initial sum (principal).

Let the principal amount be $P$ and the simple interest per year be $I$.According to the problem:
$$P+4I=2225\text{— (Equation 1)}$$
$$P+8I=2606\text{— (Equation 2)}$$
Subtracting Equation 1 from Equation 2:
$$(P+8I)-(P+4I)=2606-2225$$
$$4I=381$$
Now substitute the value of $4I$ back into Equation 1 to find $P$:
$$P+381=2225$$
$$P=2225-381=1844$$
Therefore, the initial principal sum is ₹$1,844$.