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Coupon generally refers to the interest payments that are paid, either annually or semi-annually, on debt securities like notes or bonds. Zero-coupon bonds don't make such payments, selling at a discount to their face value, also called par. They are named for a part of the paper security that investors used to redeem to receive their interest payment.
Par for the course
Until around 20 years ago, investors in corporate or government bonds would receive a bond certificate with detachable "coupons" that the investor could exchange with the issur's truistee for their interest payment - these were called 'bearer bonds'. Later came 'registered bonds', which were issued in the investor's name and automatically made coupon payments to investor, while computer-based 'book-entry bonds' are now sent to the investor's financial institution and also make automatic coupon payments.
Zero-coupon bonds, as their name suggests, do not pay coupons but instead sell at a deep discount to the face value of the bond, also known as the par value. The extent of this discount depends on both the prevailing market interest rate and the bond's maturity, which means the the price of zero-coupon bonds is more sensitive to interest-rate changes.