Q.For the bill of ₹10,000 due 6 months hence at 8% per annum, find the banker's gain.

The banker's gain is simply the gap between the banker's discount (Example 2) and the true discount (Example 3).

From the previous two examples, $BD = 400$ and $TD = 384.62$ (with $PV = 9615.38$).

Banker's gain:

Cross-check 1 (independent formula). The banker's gain equals the true discount squared over the present value:

$BG = \dfrac{TD^{2}}{PV} = \dfrac{384.62^{2}}{9615.38} = \dfrac{147932.5}{9615.38} = 15.38.$ …

$BG = TD^2/PV$ and $BG = TD\cdot rt/100$ both avoid needing the banker's discount first, so t …

Confusing banker's gain with banker's discount, or computing $BD …