Principal Amount:
The principal amount is the initial amount of money that is being invested. In this case, the principal amount is $18,000.

Rate of Interest:
The rate of interest is the percentage that is applied to the principal amount to calculate the interest. In this case, the rate of interest is 8% per annum.

Time Period:
The time period is the duration for which the principal amount is invested. In this case, the time period is 2 and a half years, which can be calculated as 2 years + 0.5 years = 2.5 years.

Compound Interest Formula:
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)

Where:
A = the final amount (including both the principal and the interest)
P = the principal amount
r = the rate of interest (in decimal form)
n = the number of times the interest is compounded per year
t = the time period (in years)

Calculation:
Given that the principal amount is $18,000, the rate of interest is 8% per annum, and the time period is 2.5 years, we can calculate the compound interest and the final amount using the compound interest formula.

Substituting the given values into the formula:
A = 18000(1 + 0.08/1)^(1*2.5)

Simplifying the formula:
A = 18000(1 + 0.08)^(2.5)

Calculating the values inside the parentheses:
A = 18000(1.08)^(2.5)

Calculating the exponent:
A = 18000(1.08^2.5)

Using a calculator to calculate 1.08^2.5, we get:
A ≈ 18000(1.2524)

Calculating the final amount:
A ≈ 22548

Compound Interest:
To calculate the compound interest, we subtract the principal amount from the final amount:
Compound Interest = A - P
Compound Interest = 22548 - 18000
Compound Interest ≈ 4548

Therefore, the compound interest on $18,000 for 2 and a half years at 8% per annum compounded annually is approximately $4,548.