Introduction:
To calculate the time it takes for a sum of money to treble itself at an 8% per annum interest rate, we need to use the compound interest formula. This formula takes into account the principal amount, the interest rate, and the compounding period to determine the final amount after a certain period of time.

Compound Interest Formula:
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including principal and interest)
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years

Step 1: Determining the interest rate and compounding period:
In this case, the interest rate is 8% per annum, which means it is compounded once per year. Therefore, n = 1.

Step 2: Calculating the number of years:
Let's assume the principal amount is P. We want to find the time it takes for the amount to treble itself, which means the final amount A will be 3P. We can substitute these values into the compound interest formula and solve for t:

3P = P(1 + 0.08/1)^(1*t)

Step 3: Simplifying the equation:
By canceling out the principal amounts and simplifying the equation, we get:

3 = (1 + 0.08)^t

Step 4: Solving for t:
To solve for t, we can take the logarithm of both sides of the equation:

log(3) = log((1 + 0.08)^t)

Using logarithmic properties, we can bring down the exponent t:

log(3) = t * log(1 + 0.08)

Finally, we can solve for t by dividing both sides of the equation by log(1 + 0.08):

t = log(3) / log(1 + 0.08)

Step 5: Calculating the value of t:
Using a calculator or logarithmic tables, we can determine the value of log(3) / log(1 + 0.08) to find the value of t.

Conclusion:
The time it takes for a sum of money to treble itself at an 8% per annum interest rate can be calculated using the compound interest formula. By substituting the given values into the formula and solving for t, we can determine the number of years it will take for the amount to triple.