# Discount basis

From ACT Wiki

This term can refer either to the cash flows of an instrument (Discount instruments) or to its basis of market quotation (Discount rate).

**Example: Discount basis calculation**

An instrument is quoted - on a __discount basis__, one period before its maturity - at a discount of 10% per period.

This means that it is currently trading at a price of 100% LESS 10% = 90% of its terminal value.

(The periodic *yield* on this instrument is 10% / 90% = 11.11%. So if the same instrument had been quoted on a __yield basis__, then the quoted yield per period = 11.11%.)

The relationship between the periodic discount rate (d) and the periodic yield (r) is:

r = d / (1 - d)

So in this case:

r = 0.10 / (1 - 0.10)

r = 0.10 / 0.90

= 11.11%