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These types of securities have more than one coupon rate and each subsequent coupon rate is higher (or lower) than the previous coupon rate. For example, a 10 year step-up note (or step down note) might have a coupon rate that is 10% for the first five years and 11% (or 9%) for the last five years or, the step-up note (or step down note) could call for a 10% coupon rate for the first three years, 10.5% (or 9.5%) for the fourth and fifth year and 11% (or 9%) for the remaining five years. When there is only one change (or step up or step down) like the first example, then it is known as a single step-up note (or step down note). When there is more than one change then it is known as a multiple step-up note (or step down note) like the second example.
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