Q.A bill of ₹10,000 is due 6 months hence. It is discounted with a banker at 8% per annum. Find

The banker's discount is just the simple interest on the face value for the 6 months still to run; the proceeds are what remains after deducting it.

Interest on ₹10,000 at 8% for half a year is ₹400, so the holder receives ₹10,000 − ₹400 = ₹9,600.

Here $F = 10000$, $r = 8\%$ per annum, and the unexpired time $t = \dfrac{6}{12} = 0.5$ year.

1. Banker's discount — simple interest on the face value:

   $BD = \dfrac{F\,r\,t}{100} = \dfrac{10000 \times 8 \times 0.5}{100} = \dfrac{40000}{100} = 400.$

2. Discounted value (proceeds):

   $F - BD = 10000 - 400 = 9600.$

   Cross-check (independent). Compute the interest directly as a fraction: $10000 \times 0.08 \times 0.5 = 10000 \times 0.04 = 400$, matching the banker's discount, and $10000 - 400 = 9600$ confirms the proceeds.
   ✓Final answer

   (i) Banker's discount = ₹400; (ii) proceeds = ₹9,600.

Using $t = 6$ (months) instead of $t = 0.5$ (years), which inflates the discount twelve-fold; or subtracting the discount from the proceeds instead of from the face value.