Banker's Discount and Discounted Value (Proceeds)

When a banker discounts a bill, the charge deducted is called the banker's discount (BD). It is simply the simple interest on the face value of the bill, calculated for the unexpired period at the agreed rate:

where $F$ is the face value, $r$ is the rate percent per annum, and $t$ is the unexpired period in years. Because the banker computes the charge on the full face value (the amount they will finally collect), the banker's discount is always slightly more than the theoretically fair charge (the true discount, §4).

The cash the holder actually receives is the face value minus this charge. This amount is called the discounted value, proceeds, or cash value of the bill:

$\text{Discounted Value (Proceeds)} = F - BD$ …