Explanation:

To find the approximate rate of simple interest per annum, let's use the simple interest formula:

- Formula: \( A = P(1 + rt) \)

- Where:

- \( A \) = Final amount

- \( P \) = Principal amount (initial sum)

- \( r \) = Rate of interest per annum

- \( t \) = Time period in years

Given that the sum becomes 6 times in 15 years, we have:

- Equation: \( 6P = P(1 + 15r) \)

- Simplifying gives \( 5P = 15Pr \)

- Simplifying further, \( r = \frac{1}{3} \)

Convert \( \frac{1}{3} \) to a percentage:

- \( r = \frac{1}{3} \times 100 = 33.33\% \)

So, the correct option is:

- Option 2: 33.33%