Q.A bank pays 10% per annum on Fixed Deposits, compounded half-yearly. Find the maturity value of a deposit of ₹25,000 held for 1 year 6 months.

For half-yearly compounding, halve the annual rate and double the time in years to get the per-period rate and the number of periods.

Periods $=2\times1.5=3$; rate per half-year $=10/2=5\%$.

$A = 25{,}000(1.05)^{3} = 25{,}000\times1.157625 = 28{,}940.63$

Here $P = ₹25{,}000$, annual rate $r = 10\%$, time $t = 1$ year 6 months $= 1.5$ years, compounded half-yearly ($n=2$).

Step 1 — Convert to half-yearly terms. Number of half-year periods $= 2t = 2\times1.5 = 3$. Rate per half-year $= \dfrac{r}{2} = \dfrac{10}{2} = 5\%$.

Step 2 — Apply the FD maturity formula.

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

Step 4 — Interest earned.

A common error is converting "1 year 6 months" to $t=1.6$ years instead of the correct $t=1.5$ years (6 months is half a year, not $0.6$ of a year) — this single conversion mistake then propagates into a wrong number of compounding periods.