Find the rate of simple interest per annum, if a sum borrowed becomes double in 5 years.

To find the rate of simple interest per annum, we can use the formula for simple interest: \[ A = P(1 + rt) \] Where: - \( A \) is the total amount after time \( t \), - \( P \) is the principal amount (the initial sum borrowed), - \( r \) is the rate of interest per annum (in decimal), - \( t \) is the time in years. In this case, we know that the sum borrowed becomes double in 5 years. Therefore, we can express this as: \[ A = 2P \] Substituting this into the simple interest formula gives us: \[ 2P = P(1 + r \cdot 5) \] Now, we can simplify this equation. First, divide both sides by \( P \) (assuming \( P \neq 0 \)): \[ 2 = 1 + 5r \] Next, we can isolate \( r \): \[ 2 - 1 = 5r \] \[ 1 = 5r \] \[ r = \frac{1}{5} \] Now, converting \( r \) into a percentage: \[ r = \frac{1}{5} \times 100\% \] \[ r = 20\% \] Thus, the rate of simple interest per annum is \( 20\% \).