Q.Find the compound interest on ₹10,000 for 3 years at 10% per annum, compounded half-yearly.

This problem uses the maximum time span allowed in this chapter — convert 3 years into half-year periods before applying the formula.

Periods $= 2 \times 3 = 6$; rate per half-year $= 10/2 = 5\%$. …

Here $P = ₹10{,}000$, $r = 10\%$ per annum, $t = 3$ years — the maximum time span this chapter's syllabus allows — compounded half-yearly, giving $2t = 6$ half-year periods at $5\%$ per period.

Step 1 — Apply the half-yearly formula.

Step 2 — Evaluate period by period. $10{,}000 \to 10{,}500 \to 11{,}025 \to 11{,}576.25 \to 12{,}155.0625 \to 12{,}762.815625 \to 13{,}400.95640625$. …

With 6 compounding periods, rounding too early at each step, rather than carrying full precision through the multiplication and rounding only the final answer, can accumulate a small but visible error — always ke …