Step 1: Define Principal and Amount

Let the principal sum be $P$. According to the question, the amount $A$ becomes $\frac{7}{5}$ of the principal in $4$ years.

$A = \frac{7}{5}P$

Step 2: Calculate Simple Interest

The simple interest $I$ is the difference between the Amount $A$ and the Principal $P$.

$I = A - P = \frac{7}{5}P - P = \frac{2}{5}P$

Step 3: Apply the Rate Formula

Substitute $I = \frac{2}{5}P$ and $T = 4$ into the rate formula $R = \frac{I \times 100}{P \times T}$.

$R = \frac{\frac{2}{5}P \times 100}{P \times 4} = \frac{200}{20} = 10\%$