Think of compound interest like a snowball rolling down a hill, where growth accumulates faster because interest is earned on both the principal and the previously accumulated interest every six months.

When interest is compounded half-yearly, the annual rate is halved and the time in years is doubled. For $1.5$ years at $10\%$ per annum, the rate becomes $5\%$ per half-year and the number of compounding periods becomes $3$. Using the amount formula $A = P(1 + \frac{R}{100})^n$, the total amount is calculated as $8000 \times (1 + \frac{5}{100})^3 = 9261$, yielding a compound interest of $9261 - 8000 = 1261$.

Always verify the compounding frequency (half-yearly, quarterly, or annually) to correctly adjust your rate and time period variables before applying formulas.