Apple Numbers INTRATE Function: Simple Annualized Maturity Returns
Explain Apple’s effective-rate wording with reproduced simple annualization, actual cash amounts and explicit day-count calculations.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
INTRATE annualizes the difference between invested cash and the cash received at maturity. Apple calls the result an “effective annual interest rate,” but its numerical example is reproduced by simple annualization, without a compounding exponent. Do not interpret that wording as a promise of compound annual growth.
Syntax and amount inputs
INTRATE(settle, maturity, invest-amount, maturity-amt, days-basis)
invest-amount is the amount paid and maturity-amt is the total received, including principal and interest. They are actual amounts in a common currency; they need not be per-100 quotes. Apple documents a nonnegative investment and a positive maturity amount. The examples below use a strictly positive investment because dividing by zero would leave the mathematical rate undefined and the article does not resolve the corresponding application behavior.
For year fraction t, the model corroborated by Apple’s example is:
annualized rate = (maturity-amt / invest-amount - 1) / t
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: 10000 becomes 10300
Enter A2 =DATE(2026,1,15), B2 =DATE(2026,7,15), C2 10000, D2 10300 and E2 0. Enter =INTRATE(A2,B2,C2,D2,E2) in F2 and format F2 as a percentage.
=INTRATE(DATE(2026,1,15),DATE(2026,7,15),10000,10300,0)
The cash gain is 300 and the holding-period return is 300/10000 = 3%. Ordinary 30/360 gives half a year, so 3%/0.5 = 6%. 6% is the independent expected annualized result; 3% remains the return over this particular holding period.
With the same cash amounts but maturity April 15, the quarter-year result is 12%. With investment 25000 and maturity amount 25750 over the original half-year, the rate remains 6%: both cash amounts were scaled by the same factor.
A basis change changes annualization
The original dates span 181 actual days. Basis 2 gives (10300/10000-1)/(181/360), approximately 5.96685082873%. Basis 3 gives the same holding-period return divided by 181/365, approximately 6.04972375691%.
Basis 4 gives 6% for these ordinary 15th-day dates. Omitting the final argument selects documented basis 0 and also gives 6% in this control. The cash gain stays 300 in every case; the annualizing time fraction changes.
Reconstruct Apple’s published rate
The official example uses investment 685 on May 1, 2009 and maturity cash 1000 on June 30, 2015, with basis 0. The 30/360 count is 2219 days:
=INTRATE(DATE(2009,5,1),DATE(2015,6,30),685,1000,0)
Independent arithmetic (1000/685-1)/(2219/360) is 0.0746045269290106, or 7.46045269290106%, matching Apple’s published number. This reconstruction is the reason to distinguish simple annualization from a compound-growth interpretation despite the word “effective.”
Advanced: compare rate conventions using the same cash flow
For the half-year 10000-to-10300 control, simple annualization is 6%. If a separate model assumes the same 3% growth repeats and compounds twice, its annual growth is 1.03^2-1 = 6.09%. That is an additional reinvestment assumption, not INTRATE’s independently reproduced formula.
Likewise, measuring the 300 gain against the 10300 maturity amount gives a redemption-based fraction, not an investment return. Keep investment amount, maturity amount, elapsed time and the chosen denominator visible when reviewing a rate.
Errors, assumptions and compatibility
Use strictly ordered dates and amounts in the same currency. Do not enter only the interest 300 in maturity-amt; the example requires total cash 10300. A percentage-formatted result of 6% is stored mathematically as 0.06.
The source’s permission for zero investment does not supply a usable finite-rate model or an exact error token. Equal dates, invalid bases, text coercion and negative cash-flow behavior were not executed. This function is not an irregular-cash-flow solver and has no sequence-of-payments or guess argument. The guide does not establish import/export or cross-platform parity.
Version, evidence and related functions
The official Apple INTRATE 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.