Why Two Day-Count Conventions Produce Different Bond Settlement Interest

A date interval is not yet an accrual fraction

Interest reconciliation needs a rule for counting days as well as a date range. FINRA Rule 11620 describes a 30-day-month, 360-day-year basis within its scope. Treasury auction formulas use the actual length of the relevant half-year period for fractional accrual on regular non-indexed notes. These references demonstrate why one generic spreadsheet formula cannot be presumed correct for every bond.

The operational question is which fraction of a specific coupon belongs in the invoice. An annual coupon, a half-year coupon and a daily amount can all represent the same obligation, but only when their denominators are consistent. Using an actual-day numerator with an unrelated assumed denominator may give a plausible-looking answer that matches neither convention. Check the security terms rather than selecting the smaller amount because it feels fairer.

Supporting references: 1. FINRA Rule 11620: Computation of Interest

Hold the dates and coupon constant

Consider an invented USD 30,000 face position paying 6 percent annually in two equal installments. Each full coupon is USD 900. Use an accrual start of January 15, 2027, a settlement boundary of March 15, 2027, and a next coupon date of July 15, 2027. Count the start but not the ending boundary for this model. The calendar interval contains 59 days, while the full actual coupon period contains 181 days.

Under a regular actual-period calculation, the accrual is USD 900 multiplied by 59 divided by 181, or approximately USD 293.37. Under a simple 30/360 treatment of these non-month-end dates, the elapsed count is 60 and the annual coupon is USD 1,800. Accrual is USD 1,800 multiplied by 60 divided by 360, or USD 300. The difference is USD 6.63 without any change in face amount or stated coupon.

Do not repair one convention with another

A third calculation uses 59 actual days divided by an assumed 180-day half-year, producing USD 295. That result sits between the other two, which can make it seem like a reasonable compromise. It is not the actual-period answer and it is not the 30/360 answer specified here. Averaging or blending conventions does not resolve a contractual calculation; it creates a different convention without authorization.

The table compares these three methods as a diagnostic. Its last column is always accrued interest in USD, and the mixed method is expressly an error candidate rather than an acceptable alternative. A small discrepancy should prompt inspection of both inputs. If a workbook assumes every month has 30 days but its date subtraction counts calendar days, the numerator and denominator no longer describe one coherent measurement.

A settlement shift changes the cash allocation

Move the modeled actual-period settlement boundary one day later, leaving the full period unchanged. Accrual becomes USD 900 times 60 divided by 181, or approximately USD 298.34. The difference is approximately USD 4.97, which is one day of the stated full-period coupon. That is a transfer of coupon entitlement between counterparties within this model, not an extra dollar of coupon created by waiting.

This sensitivity matters when a cash budget has little spare room or a confirmation uses a different settlement date from an initial estimate. It does not establish any universal number of business days between trade and settlement. Holidays, instrument rules and special transactions can change operational dates. First agree the relevant date, then count to it using the applicable convention; do not infer a legal settlement requirement from this example.

Test the periods that expose hidden assumptions

The selected January-to-March interval avoids month-end adjustments, but real calculations can face February, leap years, short first coupons and unusually long coupon periods. A formula that happens to agree on a 30-day stretch can diverge later. Test an ordinary date pair first, then a boundary case supported by the actual terms. Document what happens when the ending date falls on the final day of a month.

A practical audit sheet stores face value, annual coupon, coupon frequency, preceding coupon date, next coupon date, settlement boundary, day-count label and rounding convention. Preserve the unrounded calculation until the final step specified for that instrument. Rounding each daily amount to cents before adding days can produce a different invoice from rounding the completed accrual once. A reconciliation should identify the source of the difference rather than bury it in a miscellaneous adjustment.

Treat the reference formula as instrument-specific evidence

Treasury Appendix B discusses fractional half-year accrual and separate handling when periods cross coupon boundaries. Its presence does not establish that a corporate issue must use Treasury conventions. Equally, citing a FINRA computation rule without checking the security and transaction context cannot settle every disputed invoice. The educational purpose of the comparison is to reveal the convention choice, not provide a universal settlement calculator.

The decision boundary is operational: accept a discrepancy only after the amount reconciles to a verified convention, dates and rounding method. If a dealer supplies those inputs and the arithmetic still differs materially, request a corrected breakdown. USD 6.63 is small in this case, but repeated errors scale with face value and transaction count. The same audit discipline works without assuming any future bond return or making a tax determination.

Supporting references: 2. Treasury auction formulas: Appendix B to 31 CFR Part 356

Limits of this analysis

• Does not establish the legal scope of a settlement rule for an individual transaction.
• Actual/actual and 30/360 have variants; examples do not cover all of them.
• Irregular coupon periods, ex-interest trades and operational rounding can require other methods.