Q.A trader clears a bank overdraft of ₹20,000 by 5 equal half-yearly instalments, interest being charged at 8% per annum compounded half-yearly. Find the half-yearly instalment.

An overdraft repaid in equal instalments is amortised exactly like a loan, but the rate and the count must be taken per half-year: $i = 4\\%$ and $n = 5$ half-years.

Method 1 — Capital-recovery formula with the half-yearly rate.

8% per annum compounded half-yearly means $i = 0.04$ per half-year, and 5 half-yearly instalments means $n = 5$; $V = 20000$.

$(1.04)^{-5} = \\dfrac{1}{1.216653} = 0.821927 \\;\\Rightarrow\\; \\dfrac{1-0.821927}{0.04} = \\dfrac{0.178073}{0.04} = 4.451822$ …

Method 2 — Amortisation schedule at 4% per half-year (cross-check). Interest = opening balance × 0.04; principal = 4,492.54 − interest:

The most damaging mistake is using $i = 0.08$ and $n = 5$ (treating the 8% as the per-period rate and the 5 as years). When interest is compounded half-yearly and instalments are half-yearly, both the rate and the count must be expressed per half-year: $i = 8\\%/2 = 4\\%$ and $n …