(a) Determining the range and amount of accepted competitive bids—(1) Accepting bids. First we accept in full all non-competitive bids that were submitted by the noncompetitive bidding deadline. After the closing time for receipt of competitive bids we start accepting those at the lowest yields, discount rates, or discount margins, through successively higher yields, discount rates, or discount margins, up to the amount required to meet the offering amount. When necessary, we prorate bids at the highest accepted yield, discount rate, or discount margin as described below. If the amount of noncompetitive bids would absorb all or most of the offering amount, we will accept competitive bids in an amount sufficient to provide a fair determination of the yield, discount rate, or discount margin for the securities we are auctioning.

(2) Accepting bids at the high yield, discount rate, or discount margin. Generally, the total amount of bids at the highest accepted yield, discount rate, or discount margin exceeds the offering amount remaining after we accept the noncompetitive bids and the competitive bids at the lower yields, discount rates, or discount margins. In order to keep the total amount of awards as close as possible to the announced offering amount, we award a percentage of the bids at the highest accepted yield, discount rate, or discount margin. We derive the percentage by dividing the remaining par amount needed to fill the offering amount by the par amount of the bids at the high yield, discount rate, or discount margin and rounding up to the next hundredth of a whole percentage point, for example, 17.13%.

(b) Determining the interest rate for new non-indexed and inflation-protected note and bond issues. If a Treasury non-indexed or inflation-protected note or bond auction results in a yield lower than 0.125 percent, the interest rate will be set at 1/8 of one percent, and successful bidders' award prices will be calculated accordingly. (See appendix B to this part for formulas.)

(1) Single-price auctions. The interest rate we establish produces the price closest to, but not above, par when evaluated at the yield of awards to successful competitive bidders.

(2) Multiple-price auctions. The interest rate we establish produces the price closest to, but not above, par when evaluated at the weighted-average yield of awards to successful competitive bidders.

(c) Determining the interest rate for floating rate notes. The interest rate will be the spread plus the index rate (as it may be adjusted on the calendar day following each auction of 13-week bills) subject to a minimum daily interest accrual rate of zero percent.

(d) Determining purchase prices for awarded securities. We round price calculations to six decimal places on the basis of price per hundred, for example, 99.954321 (See appendix B to this part).

(1) Single-price auctions. We award securities to both noncompetitive and competitive bidders at the price equivalent to the highest accepted yield, discount rate, or discount margin at which bids were accepted. For inflation-protected securities, the price for awarded securities is the price equivalent to the highest accepted real yield.

(2) Multiple-price auctions—(i) Competitive bids. We award securities to competitive bidders at the price equivalent to each yield, discount rate, or discount margin at which their bids were accepted.

(ii) Noncompetitive bids. We award securities to noncompetitive bidders at the price equivalent to the weighted average yield, discount rate, or discount margin of accepted competitive bids.