Q.Find the amount and the compound interest on ₹8,000 for 1½ years at 10% per annum, compounded half-yearly.

For half-yearly compounding, halve the rate and double the number of periods: $r = 5\%$ per half-year and $m = 3$ half-years.

Given: $P = 8000$, nominal $R = 10\%$ p.a., $T = 1.5$ years, compounded half-yearly.

Adjust for half-yearly compounding. Rate per period $r = \dfrac{10}{2} = 5\%$; number of periods $m = 2 \times 1.5 = 3$.

Method 1 — formula.

So $CI = A - P = 9261 - 8000 = 1261$.

Method 2 — independent check (period-by-period).

• After 1st half-year: $8000 \times 1.05 = 8400$. …

Using R = 10 and n = 1.5 without adjusting for half-yearly compounding. The rate must be halved (to 5%) and the number of periods …