31 C.F.R. § 306 app to Subpart E of Part 306
computation of interest on annual basis
One Day's Interest is 1/365 or 1/366 of 1-Year's Interest
Computation of interest on Treasury bonds, notes, and certificates of indebtedness will be made on an annual basis in all cases where interest is payable in one amount for the full term of the security, unless such term is an exact half-year (6 months), and it is provided that interest shall be computed on a semi-annual basis.
If the term of the securities is exactly 1 year, the interest is computed for the full period at the specified rate regardless of the number of days in such period.
If the term of the securities is less than 1 full year, the annual interest period for purposes of computation is considered to be the full year from but not including the date of issue to and including the anniversary of such date.
If the term of the securities is more than 1 full year, computation is made on the basis of one full annual interest period, ending with the maturity date, and a fractional part of the preceding full annual interest period.
The computation of interest for any fractional part of an annual interest period is made on the basis of 365 actual days in such period, or 366 days if February 29 falls within such annual period.
computation of interest on semiannual basis
One Day's Interest is 1/181, 1/182, 1/183 or 1/184 or 1/2 Year's Interest
Computation of interest on Treasury bonds, notes, and certificates of indebtedness will be made on a semiannual basis in all cases where interest is payable for one or more full half-year (6 months) periods, or for one or more full half-year periods and a fractional part of a half-year period. A semiannual interest period is an exact half-year or 6 months, for computation purposes, and may comprise 181, 182, 183 or 184 actual days.
An exact half-year's interest at the specified rate is computed for each full period of exactly 6 months, irrespective of the actual number of days in the half-year.
If the initial interest covers a fractional part of a half-year, computation is made on the basis of the actual number of days in the half-year (exactly 6 months) ending on the day such initial interest becomes due. If the initial interest covers a period in excess of 6 months, computation is made on the basis of one full half-year, ending with the interest due date, and a fractional part of the preceding full half-year period.
Interest for any fractional part of a full half-year period is computed on the basis of the exact number of days in the full period, including February 29 whenever it falls within such a period.
The number of days in any half-year period is shown in the following table:
For the Half-Year
| Interest period | Beginning and ending days are 1st or 15th of months listed under interest period (number of days) | Beginning and ending days are last days of months listed under interest period (number of days) | ||
| Regular year | Leap year | Regular year | Leap year | |
| January to July | 181 | 182 | 181 | 182 |
| February to August | 181 | 182 | 184 | 184 |
| March to September | 184 | 184 | 183 | 183 |
| April to October | 183 | 183 | 184 | 184 |
| May to November | 184 | 184 | 183 | 183 |
| June to December | 183 | 183 | 184 | 184 |
| July to January | 184 | 184 | 184 | 184 |
| August to February | 184 | 184 | 181 | 182 |
| September to March | 181 | 182 | 182 | 183 |
| October to April | 182 | 183 | 181 | 182 |
| November to May | 181 | 182 | 182 | 183 |
| December to June | 182 | 183 | 181 | 182 |
| 1 year (any 2 consecutive half-years) | 365 | 366 | 365 | 366 |
The following are dates for end-of-the-month interest computations.
| When interest period ends on- | Interest-computation period will be from but will not include- |
| January 31 | July 31. |
| February 28 in 365-day year. | August 31. |
| February 29 | Do. |
| March 30, 31 | September 30. |
| April 30 | October 31. |
| May 30, 31 | November 30. |
| June 30 | December 31. |
| July 31 | January 31. |
| August 29, 30, or 31 | February 28 in 365-day year. |
| February 29 in leap year. | |
| September 30 | March 31. |
| October 30, 31 | April 30. |
| November 30 | May 31. |
| December 30, 31 | June 30. |
use OF INTEREST TABLES
In the appended tables decimals are set forth for use in computing interest for fractional parts of interest periods. The decimals cover interest on $1,000 for 1 day in each possible semiannual (Table I), and annual (Table II) interest period, at all rates of interest, in steps of 1/8 percent, from 1/8 to 9 percent. The amount of interest accruing on any date (for a fractional part of an interest period) on $1,000 face amount of any issue of Treasury bonds, Treasury notes, or Treasury certificates of indebtedness may be ascertained in the following way:
(1) The date of issue, the dates for the payment of interest, the basis (semiannual or annual) upon which interest is computed, and the rate of interest (percent per annum) may be determined from the text of the security, or from the official circular governing the issue.
(2) Determine the interest period of which the fraction is a part, and calculate the number of days in the full period to determine the proper column to be used in selecting the decimal for 1 day's interest.
(3) Calculate the actual number of days in the fractional period from but not including the date of issue or the day on which the last preceding interest payment was made, to and including the day on which the next succeeding interest payment is due or the day as of which the transaction which terminates the accrual of additional interest is effected.
(4) Multiply the appropriate decimal (1 day's interest on $1,000) by the number of days in the fractional part of the interest period. The appropriate decimal will be found in the appended table for interest payable semiannually or annually, as the case may be, opposite the rate borne by the security, and in the column showing the full interest period of which the fractional period is a part. (For interest on any other amount, multiply the amount of interest on $1,000 by the other amount expressed as a decimal of $1,000.)
treasury
The methods of computing discount rates on U.S. Treasury bills are given below:
Computation will be made on an annual basis in all cases. The annual period for bank discount is a year of 360 days, and all computations of such discount will be made on that basis. The annual period for true discount is 1 full year from but not including the date of issue to and including the anniversary of such date. Computation of true discount for a fractional part of a year will be made on the basis of 365 days in the year, or 366 days if February 29 falls within the year.
bank discount
The bank discount rate on a Treasury bill may be ascertained by: (1) Subtracting the sale price of the bill from its face value to obtain the amount of discount; (2) dividing the amount of discount by the number of days the bill is to run to obtain the amount of discount per day; (3) multiplying the amount of discount per day by 360 (the number of days in a commercial year of 12 months of 30 days each) to obtain the amount of discount per year; and (4) dividing the amount of discount per year by the face value of the bill to obtain the bank discount rate.
For example:
| 91-day bill: | |
| Principal amount-maturity value | $100.00 |
| Price at issue-amount received | 99.50 |
| Amount of discount | .50 |
| $0.50 ÷ 91 * 360 ÷ $100 = .01978 or 1.978 percent |
true discount
The true discount rate on a Treasury bill of not more than one-half year in length may be ascertained by (1 and 2) obtaining the amount of discount per day by following the first two steps described under "Bank Discount"; (3) multiplying the amount of discount per day by the actual number of days in the year from date of issue (365 ordinarily, but 366 if February 29 falls within the year from date of issue) to obtain the amount of discount per year; and (4) dividing the amount of discount per year by the sale price of the bill to obtain the true discount rate.
For example:
| 91-day bill: | |
| Principal amount-maturity value | $100.00 |
| Price at issue-amount received | 99.50 |
| Amount of discount | .50 |
| $0.50 ÷ 91 * 365 ÷ $99.50 = .02016 or 2.016 percent |
Table I-Decimal for 1 Day's Interest on $1,000 at Various Rates of Interest, Payable Semiannually or on a Semiannual Basis, in Regular Years of 365 Days and in Leap Years of 366 Days (to Determine Applicable Number of Days, See "Computation of Interest on Semiannual Basis")
| Rate per annum (percent) | Half-year of 184 days | Half-year of 183 days | Half-year of 182 days | Half-year of 181 days |
| 1/8 | $0.003 396 739 | $0.003 415 301 | $0.003 434 066 | $0.003 453 039 |
| 1/4 | .006 793 478 | .006 830 601 | .006 868 132 | .006 906 077 |
| 3/8 | .010 190 217 | .010 245 902 | .010 302 198 | .010 359 116 |
| 1/2 | .013 586 957 | .013 661 202 | .013 736 264 | .013 812 155 |
| 5/8 | .016 983 696 | .017 076 503 | .017 170 330 | .017 265 193 |
| 3/4 | .020 380 435 | .020 491 803 | .020 604 396 | .020 718 232 |
| 7/8 | .023 777 174 | .023 907 104 | .024 038 462 | .024 171 271 |
| 1 | .027 173 913 | .027 322 404 | .027 472 527 | .027 624 309 |
| 11/8 | .030 570 652 | .030 737 705 | .030 906 593 | .031 077 348 |
| 11/4 | .033 967 391 | .034 153 005 | .034 340 659 | .034 530 387 |
| 13/8 | .037 364 130 | .037 568 306 | .037 774 725 | .037 983 425 |
| 11/2 | .040 760 870 | .040 983 607 | .041 208 791 | .041 436 464 |
| 15/8 | .044 157 609 | .044 398 907 | .044 642 857 | .044 889 503 |
| 13/4 | .047 554 348 | .047 814 208 | .048 076 923 | .048 342 541 |
| 17/8 | .050 951 087 | .051 229 508 | .051 510 989 | .051 795 580 |
| 2 | .054 347 826 | .054 644 809 | .054 945 055 | .055 248 619 |
| 21/8 | .057 744 565 | .058 060 109 | .058 379 121 | .058 701 657 |
| 21/4 | .061 141 304 | .061 475 410 | .061 813 187 | .062 154 696 |
| 23/8 | .064 538 043 | .064 890 710 | .065 247 253 | .065 607 735 |
| 21/2 | .067 934 783 | .068 306 011 | .068 681 319 | .069 060 773 |
| 25/8 | .071 331 522 | .071 721 311 | .072 115 385 | .072 513 812 |
| 23/4 | .074 728 261 | .075 136 612 | .075 549 451 | .075 966 851 |
| 27/8 | .078 125 000 | .078 551 913 | .078 983 516 | .079 419 890 |
| 3 | .081 521 739 | .081 967 213 | .082 417 582 | .082 872 928 |
| 31/8 | .084 918 478 | .085 382 514 | .085 851 648 | .086 325 967 |
| 31/4 | .088 315 217 | .088 797 814 | .089 285 714 | .089 779 006 |
| 33/8 | .091 711 957 | .092 213 115 | .092 719 780 | .093 232 044 |
| 31/2 | .095 108 696 | .095 628 415 | .096 153 846 | .096 685 083 |
| 35/8 | .098 505 435 | .099 043 716 | .099 021 978 | .100 138 122 |
| 33/4 | .101 902 174 | .102 459 016 | .103 021 978 | .103 591 160 |
| 37/8 | .105 298 913 | .105 874 317 | .106 456 044 | .107 044 190 |
| 4 | .108 695 652 | .109 289 617 | .109 890 110 | .110 497 238 |
| 41/8 | .112 092 391 | .112 704 918 | .113 324 176 | .113 950 236 |
| 41/4 | .115 489 130 | .116 120 219 | .116 758 242 | .117 403 375 |
| 43/8 | .118 885 870 | .119 535 519 | .120 192 308 | .120 856 317 |
| 41/2 | .122 282 609 | .122 950 820 | .123 626 374 | .124 309 394 |
| 45/8 | .125 679 348 | .126 366 120 | .127 060 440 | .127 762 432 |
| 43/4 | .129 076 087 | .129 781 421 | .130 494 505 | .131 215 471 |
| 47/8 | .132 472 826 | .133 196 721 | .133 928 571 | .134 668 500 |
| 5 | .135 869 565 | .136 612 022 | .137 362 637 | .138 121 548 |
| 51/8 | .139 266 304 | .140 027 322 | .140 796 703 | .141 574 586 |
| 51/4 | .142 663 043 | .143 442 623 | .144 230 769 | .145 027 624 |
| 53/8 | .146 059 783 | .146 857 923 | .147 664 835 | .148 480 663 |
| 51/2 | .149 456 522 | .150 273 224 | .151 098 901 | .151 933 702 |
| 55/8 | .152 853 261 | .153 688 525 | .154 532 967 | .155 386 748 |
| 53/4 | .156 250 000 | .157 103 825 | .157 967 033 | .158 839 706 |
| 57/8 | .159 646 739 | .160 519 126 | .161 401 099 | .162 292 876 |
| 6 | .163 043 478 | .163 934 426 | .164 835 165 | .165 745 856 |
| 61/8 | 166 440 217 | .167 349 727 | .168 269 231 | .169 198 895 |
| 61/4 | .169 836 957 | .170 765 027 | .171 703 297 | .172 651 934 |
| 63/8 | .173 233 696 | .174 180 328 | .175 137 363 | .176 104 972 |
| 61/2 | .176 630 435 | .177 595 628 | .178 571 429 | .179 558 011 |
| 65/8 | .180 027 174 | .181 010 929 | .182 005 495 | .183 011 050 |
| 63/4 | .183 423 913 | .184 426 230 | .185 439 560 | .186 464 088 |
| 67/8 | .186 820 652 | .187 841 530 | .188 873 626 | .189 917 127 |
| 7 | .190 217 391 | .191 256 831 | .192 307 692 | .193 370 166 |
| 71/8 | .193 614 130 | .194 672 131 | .195 741 758 | .196 823 204 |
| 71/4 | .197 010 870 | .198 087 432 | .199 175 824 | .200 276 243 |
| 73/8 | .200 407 609 | .201 502 732 | .202 609 890 | .203 729 282 |
| 71/2 | .203 804 348 | .204 918 033 | .206 043 956 | .207 182 320 |
| 75/8 | .207 201 087 | .208 333 333 | .209 478 022 | .210 635 359 |
| 73/4 | .210 597 826 | .211 748 634 | .212 912 088 | .214 088 398 |
| 77/8 | .213 994 565 | .215 163 934 | .216 346 154 | .217 541 436 |
| 8 | .217 391 304 | .218 579 235 | .219 780 220 | .220 994 475 |
| 81/8 | .220 788 043 | .221 994 536 | .223 214 286 | .224 447 514 |
| 81/4 | .224 184 783 | .225 409 836 | .226 648 352 | .227 900 552 |
| 83/8 | .227 581 522 | .228 825 137 | .230 082 418 | .231 353 591 |
| 81/2 | .230 978 261 | .232 240 437 | .233 516 484 | .234 806 630 |
| 85/8 | .234 375 000 | .235 655 738 | .236 950 549 | .238 259 669 |
| 83/4 | .237 771 739 | .239 071 038 | .240 384 615 | .241 712 707 |
| 87/8 | .241 168 478 | .242 486 339 | .243 818 681 | .245 165 746 |
| 9 | .244 565 217 | .245 901 639 | .247 252 747 | .248 618 785 |
| 91/8 | .247 961 957 | .249 316 940 | .250 686 813 | .252 071 823 |
| 91/4 | .251 358 696 | .252 732 240 | .254 120 879 | .255 524 862 |
| 93/8 | .254 755 435 | .256 147 541 | .257 554 945 | .258 977 901 |
| 91/2 | .258 152 174 | .259 562 842 | .260 989 011 | .262 430 939 |
| 95/8 | .261 548 913 | .262 978 142 | .264 423 077 | .265 883 978 |
| 93/4 | .264 945 652 | .266 393 443 | .267 857 143 | .269 337 017 |
| 97/8 | .268 342 391 | .269 808 743 | .271 291 209 | .272 790 055 |
| 10 | .271 739 130 | .273 224 044 | .274 725 275 | .276 243 094 |
| 101/8 | .275 135 870 | .276 639 344 | .278 159 341 | .279 696 133 |
| 101/4 | .278 853 609 | .280 054 645 | .281 593 407 | .283 149 171 |
| 103/8 | .281 929 348 | .283 469 945 | .285 027 473 | .286 602 210 |
| 101/2 | .285 326 087 | .286 885 246 | .288 461 538 | .290 055 249 |
| 105/8 | .288 722 826 | .290 300 546 | .291 895 604 | .293 508 287 |
| 103/4 | .292 119 565 | .293 715 847 | .295 329 670 | .296 961 326 |
| 107/8 | .295 516 304 | .297 131 148 | .298 763 736 | .300 414 365 |
| 11 | .298 913 043 | .300 546 448 | .302 197 802 | .303 867 403 |
| 111/8 | .302 309 783 | .303 961 749 | .305 631 868 | .307 320 442 |
| 111/4 | .305 706 522 | .307 377 049 | .309 065 934 | .310 773 481 |
| 113/8 | .309 103 261 | .310 792 350 | .312 500 000 | .314 226 519 |
| 111/2 | .312 500 000 | .314 207 650 | .315 934 066 | .317 679 558 |
| 115/8 | .315 896 739 | .317 622 951 | .319 368 132 | .321 132 597 |
| 113/4 | .319 293 478 | .321 038 251 | .322 802 198 | .324 585 635 |
| 117/8 | .322 690 217 | .324 453 552 | .326 236 264 | .328 038 674 |
| 12 | .326 086 957 | .327 868 852 | .329 670 330 | .331 491 713 |
Table II-Decimal for 1 Day's Interest on $1,000 at Various Rates of Interest, Payable Annually or on an Annual Basis, in Regular Years of 365 Days and in Leap Years of 366 Days
| Rate per annum (percent) | Regular year, 365 days | Leap year, 366 days |
| 1/8 | $0.003 424 658 | $0.003 415 301 |
| 1/4 | .006 849 315 | .006 830 601 |
| 3/8 | .010 273 973 | .010 245 902 |
| 1/2 | .013 698 630 | .013 661 202 |
| 5/8 | .017 123 288 | .017 076 503 |
| 3/4 | .020 547 945 | .020 491 803 |
| 7/8 | .023 972 603 | .023 907 104 |
| 1 | .027 397 260 | .027 322 404 |
| 11/8 | .030 821 918 | .030 737 705 |
| 11/4 | .034 246 575 | .034 153 005 |
| 13/8 | .037 671 233 | .037 568 306 |
| 11/2 | .041 095 890 | .040 983 607 |
| 15/8 | .044 520 548 | .044 398 907 |
| 13/4 | .047 945 205 | .047 814 208 |
| 17/8 | .051 369 863 | .051 229 508 |
| 2 | .054 794 521 | .054 644 809 |
| 21/8 | .058 219 178 | .058 060 109 |
| 21/4 | .061 643 836 | .061 475 410 |
| 23/8 | .065 068 493 | .064 890 710 |
| 21/2 | .068 493 151 | .068 306 011 |
| 25/8 | .071 917 808 | .071 721 311 |
| 23/4 | .075 342 466 | .075 136 612 |
| 27/8 | .078 767 123 | .078 551 913 |
| 3 | .082 191 781 | .081 967 213 |
| 31/8 | .085 616 438 | .085 382 514 |
| 31/4 | .089 041 096 | .088 797 814 |
| 33/8 | .092 465 753 | .092 213 115 |
| 31/2 | .095 890 411 | .095 628 415 |
| 35/8 | .099 315 068 | .099 043 716 |
| 33/4 | .102 739 726 | .102 459 016 |
| 37/8 | .106 164 384 | .105 874 317 |
| 4 | .109 589 041 | .109 289 617 |
| 41/8 | .113 013 699 | .112 704 918 |
| 41/4 | .116 438 356 | .116 120 219 |
| 43/8 | .119 863 014 | .119 535 519 |
| 41/2 | .123 287 671 | .122 950 820 |
| 45/8 | .126 712 329 | .126 366 120 |
| 43/4 | .130 136 986 | .129 781 421 |
| 47/8 | .133 561 644 | .133 196 721 |
| 5 | .136 986 301 | .136 612 022 |
| 51/8 | .140 410 959 | .140 027 322 |
| 51/4 | .143 835 616 | .143 442 623 |
| 53/8 | .147 260 274 | .146 857 923 |
| 51/2 | .150 684 932 | .150 273 224 |
| 55/8 | .154 109 589 | .153 688 525 |
| 53/4 | .157 534 247 | .157 103 825 |
| 57/8 | .160 958 904 | .160 519 126 |
| 6 | .164 383 562 | .163 934 426 |
| 61/8 | .167 808 219 | .167 349 727 |
| 61/4 | .171 232 877 | .170 765 027 |
| 63/8 | .174 657 534 | .174 180 328 |
| 61/2 | .178 082 192 | .177 595 628 |
| 65/8 | .181 506 849 | .181 010 929 |
| 63/4 | .184 931 507 | .184 426 230 |
| 67/8 | .188 356 164 | .187 841 530 |
| 7 | .191 780 822 | .191 256 831 |
| 71/8 | .195 205 479 | .194 672 131 |
| 71/4 | .198 630 137 | .198 087 432 |
| 73/8 | .202 054 795 | .201 502 732 |
| 71/2 | .205 479 452 | .204 918 033 |
| 75/8 | .208 904 110 | .208 333 333 |
| 73/4 | .212 328 767 | .211 748 634 |
| 77/8 | .215 753 425 | .215 163 934 |
| 8 | .219 178 082 | .218 579 235 |
| 81/8 | .222 602 740 | .221 994 536 |
| 81/4 | .226 027 397 | .225 409 836 |
| 83/8 | .229 452 055 | .228 825 137 |
| 81/2 | .232 876 712 | .232 240 437 |
| 85/8 | .236 301 370 | .235 655 738 |
| 83/4 | .239 726 027 | .239 071 038 |
| 87/8 | .243 150 685 | .242 486 339 |
| 9 | .246 575 342 | .245 901 639 |
| 91/8 | .250 000 000 | .249 316 940 |
| 91/4 | .253 424 658 | .252 732 240 |
| 93/8 | .256 849 315 | .256 147 541 |
| 91/2 | .260 273 973 | .259 562 842 |
| 95/8 | .263 698 630 | .262 978 142 |
| 93/4 | .267 123 288 | .266 393 443 |
| 97/8 | .270 547 945 | .269 808 743 |
| 10 | .273 972 603 | .273 224 044 |
| 101/8 | .277 397 260 | .276 639 344 |
| 101/4 | .280 821 918 | .280 054 645 |
| 103/8 | .284 246 575 | .283 469 945 |
| 101/2 | .287 671 233 | .286 885 246 |
| 105/8 | .291 095 890 | .290 300 546 |
| 103/4 | .294 520 548 | .293 715 847 |
| 107/8 | .297 945 205 | .297 131 148 |
| 11 | .301 369 863 | .300 546 448 |
| 111/8 | .304 794 521 | .303 961 749 |
| 111/4 | .308 219 178 | .307 377 049 |
| 113/8 | .311 643 836 | .310 792 350 |
| 111/2 | .315 068 493 | .314 207 650 |
| 115/8 | .318 493 151 | .317 622 951 |
| 113/4 | .321 917 808 | .321 038 251 |
| 117/8 | .325 342 466 | .324 453 552 |
| 12 | .328 767 123 | .327 868 852 |
31 C.F.R. 306 app to Subpart E of Part 306