Q.A sum of ₹8,000 is invested at 10% per annum, compounded half-yearly, for 1 year 6 months. Find the amount and the compound interest.

For half-yearly compounding, halve the rate and double the number of periods before applying the compound-interest formula.

Number of half-year periods $= 2 \times 1.5 = 3$; rate per half-year $= 10/2 = 5\%$.

$A = 8{,}000(1.05)^{3} = 8{,}000 \times 1.157625 = 9{,}261$

$CI = 9{,}261 - 8{,}000 = 1{,}261$

Here $P = ₹8{,}000$, annual rate $r = 10\%$, time $t = 1$ year 6 months $= 1.5$ years, compounded half-yearly.

Step 1 — Convert to half-yearly terms. Number of half-year periods $= 2t = 2 \times 1.5 = 3$. Rate per half-year $= \dfrac{r}{2} = \dfrac{10}{2} = 5\%$.

Step 2 — Apply the half-yearly formula.

Step 3 — Evaluate. $(1.05)^3 = 1.157625$, so

Step 4 — Compound interest.

A frequent slip is halving the rate but forgetting to double the time, or the reverse — e.g. using $(1.05)^{1.5}$ or $(1.10)^{3}$ instead of $(1.05)^3$. The rate-per-period and the number-of-periods must both be converted together to match the compounding frequency.