Apple Numbers DISC Function: Discount Rates and Redemption-Based Quotes
Calculate redemption-based annual discount rates, compare day bases and distinguish discount from investment return with complete examples.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
DISC returns an annual discount rate for a non-interest-paying security purchased below redemption value. Its discount is measured against redemption, rather than against the cash invested. That denominator choice matters even when both results are formatted as percentages.
Syntax and quote units
DISC(settle, maturity, price, redemption, days-basis)
Apple requires positive price and redemption. Both are quotes per 100 of face value: divide the cash amount by face value, then multiply by 100. Redemption is often 100, but it is an explicit argument. The result is a rate, so format it as a percentage without multiplying the underlying value by 100 again.
For the ordinary-date controls, let t be the selected year fraction. The arithmetic that reproduces Apple’s example is:
discount rate = (redemption - price) / redemption / t
There is no compounding exponent in this calculation.
Dates and day-count basis
Use date-valued cells or DATE(year,month,day) rather than ambiguous text such as 1/2/2026. Settlement is the trade’s settlement date, which need not be its trade date. Apple requires maturity to be later than settlement.
The optional final argument selects:
| Basis | Convention |
|---|---|
| 0, or omitted | NASD 30/360 |
| 1 | Actual/actual |
| 2 | Actual/360 |
| 3 | Actual/365 |
| 4 | European 30/360 |
Basis 0 and basis 4 have different month-end rules. Agreement on the ordinary dates below does not make them interchangeable. The actual-day controls count elapsed calendar days; they do not add an extra day for including both endpoints. These examples do not establish every February-end adjustment or the treatment of a multi-year actual/actual interval.
Step by step: a six-month discount
Enter A2 =DATE(2026,1,15), B2 =DATE(2026,7,15), C2 98, D2 100 and E2 0. In F2 enter =DISC(A2,B2,C2,D2,E2).
The complete literal version is:
=DISC(DATE(2026,1,15),DATE(2026,7,15),98,100,0)
Under ordinary 30/360 arithmetic the interval is 180/360, or half a year. The discount is 2 per 100 redeemed, so (2/100)/0.5 = 0.04: 4%. This is an independently calculated expectation.
With price 96 and the other inputs unchanged, the result is 8%. With price 98 but maturity April 15, 2026, the same two-unit discount occurs over 90/360 of a year and also annualizes to 8%. Price changes and time changes are separate reasons for a changed annualized result.
Compare the same dates under different bases
January 15 to July 15, 2026 contains 181 actual days. Holding price 98 and redemption 100 fixed gives:
| Basis | Year fraction | Independent rate |
|---|---|---|
| 0 or omitted | 180/360 | 4% |
| 2 | 181/360 | 3.97790055249% |
| 3 | 181/365 | 4.03314917127% |
| 4 | 180/360 | 4% |
A larger time fraction reduces the annualized rate for the same fixed discount. The agreement of bases 0 and 4 here reflects the 15th-day dates, not a universal identity.
Reproduce the official longer example
Apple uses settlement May 1, 2009, maturity June 30, 2015, price 67.14, redemption 100 and basis 0. The ordinary 30/360 numerator is 2219 days. Thus:
(1-67.14/100)/(2219/360) = 0.0533105002253267
That is 5.33105002253%, reproducing the published rounded 5.33%. The corresponding formula is =DISC(DATE(2009,5,1),DATE(2015,6,30),67.14,100,0). Treat the extra digits as independent arithmetic, not a promise about every Numbers display or calculation precision.
Advanced: reconcile quotes with a position
For a fictional face amount of 25000, price 98 means cash cost 24500, and redemption 100 means maturity cash 25000. The gain is 500. Discount annualization uses 500/25000/0.5 = 4%.
Annualizing the gain relative to the invested 24500 instead gives 500/24500/0.5, approximately 4.08163265306%. That investment-based measure has a different denominator. A compound annual growth calculation would introduce yet another convention. None should be substituted for DISC merely because all are annual percentages.
Errors and practical checks
Reject reversed dates and nonpositive quote inputs in your model before calculating. Entering cash cost 24500 together with redemption quote 100 mixes units and makes the result meaningless. Either normalize both amounts to per-100 quotes or keep a separate cash-flow calculation with consistent units.
The checked article does not enumerate exact error tokens, coercion rules or fractional basis handling. A purchase above redemption is outside the discount-security examples here; no untested error behavior is asserted. These examples omit fees, taxes and reinvestment assumptions and are function education, not investment recommendations.
Version, evidence and related functions
The official Apple DISC reference was checked on October 18, 2026 in Formulas and Functions Help 15.4, within the Numbers 15.4 for Mac documentation context. The worked values in this guide are independent calculations; Apple’s published example is identified separately. No Numbers session or other spreadsheet calculation engine was executed. Cell-reference walkthroughs are instructions, not recorded application tests.
The first release introducing this function is unknown from the checked evidence. The current reference documents it; it does not label it deprecated or retired. Shared iWork documentation does not independently verify every platform, older release or import/export path.