The price P of an FRN per $100 face value is given by the expression

where

• R_T is the reference rate at the last coupon reset date T;
• M is the reset margin;
• DM is the discount margin;
• r is the zero rate at the next coupon payment date;
• d is the number of days in the current interest period;
• f is the number of days from settlement date to next coupon date;
• a_n = (1 − vⁿ)/i;
• v = 1/(1 + i);
• i = (S + DM)/n;
• S is the annual swap rate from settlement to maturity of the FRN;
• n is the number of interest periods to maturity at the next coupon date.

Quarterly coupons and a 365-day year are assumed.

The expression is easier to understand if each term is examined separately:

• is the next coupon payment;
• is the present value, at the next coupon date, of the difference between the reset margin and the current discount margin, for all future payments, as an annuity (a series of equal payments at regular intervals);
• discounts the values of these payments back to the present.