To find the rate of simple interest when the interest is equal to the sum invested over a period of 4 years, we can use the formula for simple interest:
\[ I = P \times r \times t \]
where:
- \( I \) is the interest,
- \( P \) is the principal amount (the sum invested),
- \( r \) is the rate of interest (in decimal),
- \( t \) is the time in years.
Given that the interest \( I \) is equal to the principal \( P \) after 4 years, we can set up the following equation:
\[ P = P \times r \times 4 \]
We can divide both sides by \( P \) (assuming \( P \neq 0 \)):
\[ 1 = r \times 4 \]
Now we solve for \( r \):
\[ r = \frac{1}{4} = 0.25 \]
To express \( r \) as a percentage, we multiply by 100:
\[ r = 0.25 \times 100 = 25% \]
Thus, the rate of simple interest is 25%.