A sum at simple interest of $7\%$ per annum amounts to $\text{Rs. }4,368$ in $8$ years. Find the sum.

Let the principal (sum) be $P$.Given:Rate ($R$) = $7\%$ per annumTime ($T$) = $8$ yearsAmount ($A$) = $\text{Rs. }4,368$ The relationship between Amount and Principal under simple interest is:
$$A=P+\text{SI}$$
$$A=P+\frac{P\times R\times T}{100}$$
$$A=P\left(1+\frac{R\times T}{100}\right)$$
Substitute the given values into the formula:
$$4368=P\left(1+\frac{7\times 8}{100}\right)$$
$$4368=P\left(1+\frac{56}{100}\right)$$
$$4368=P\left(\frac{156}{100}\right)$$
Now, solving for $P$:
$$P=\frac{4368\times 100}{156}$$
$$P=28\times 100=2800$$
Thus, the sum is $\text{Rs. }2,800$.