Apple Numbers DB: Fixed-Declining Depreciation and Partial First Years

• Introduced: Documented in Apple’s Formulas and Functions Help 15.4; the original release and introduction date remain unknown.
• Availability: Currently documented in Apple’s Functions Help 15.4 documentation edition; no final supported-version endpoint is established.
• Scope: Shared iWork reference. Individual Mac, iPad, iPhone and iCloud build availability and historical behavior are not established here.
• Checked: October 14, 2026, against the official DB reference. Documentation and independent depreciation models; no native Numbers test.

=DB(cost, salvage, life, depr-period, first-year-months)

Cost and salvage are required numeric amounts, each at least zero. Life is the required useful life in periods and must be greater than zero; Apple allows a fractional life. Depr-period is the required period to calculate, must be greater than zero, and has any fractional part ignored.

First-year-months is optional and must be between 1 and 12 when supplied; its fractional part is ignored. Apple’s entry does not state its omitted-argument default, so the examples here supply it explicitly. Do not assume an optional argument has a particular default merely because another spreadsheet does.

The first four inputs describe the asset and the period being calculated. DB returns that period’s charge, rather than a cumulative total or remaining book value. Currency display follows the document’s regional settings; it does not change the arithmetic or select a tax policy.

Create a Numbers table named FixedDeclining, with five columns A:E and five rows including one header row. Put Year, DB charge, Rate-model charge, Model opening balance and Model closing balance in A1:E1. Enter 1, 2, 3, 4 in A2:A5.

In B2 enter =DB(1000,100,4,A2,12) and fill to B5. Apple’s published currency outputs are:

A rate of 43.8% reproduces this schedule. To show that check separately, put 1000 in D2, =D2*43.8% in C2 and =D2-C2 in E2. Put =E2 in D3, =D3*43.8% in C3 and =D3-C3 in E3, then fill C3:E3 through row 5.

Expected model closing balances are 562, 315.844, 177.504328 and 99.757432336. The model’s full-precision charges round to Apple’s published cents, but the page does not establish DB’s general internal rate-rounding rule. The 43.8% recurrence is an independent reconstruction of this particular example.

The model does not end at exactly the entered salvage of 100. Do not silently force its last charge to a different amount or infer that all depreciation functions handle rounding and salvage identically. Rounding every intermediate charge to cents would also create a different calculation.

Keep the schedule intact. Create a separate table named FirstYear, with three columns A:C and five rows. Use Months supplied, DB first-year charge and Proportional check as the headers. Enter 12, 9, 6, 9.9 in A2:A5.

Enter =DB(1000,100,4,1,A2) in B2 and fill to B5. The independently expected values are 438, 328.5, 219, 328.5. The first three are Apple’s literal examples; the last follows its rule that the month’s fractional part is ignored.

Enter the comparison formulas separately:

• C2: =438*12/12 → 438
• C3: =438*9/12 → 328.5
• C4: =438*6/12 → 219
• C5: =438*9/12 → 328.5

The 9.9 input does not request a 9.9-month fractional charge under the documented truncation rule. These controls cover the first year; they do not establish a universal final partial-year or out-of-life-period rule.

Create another table named HalfRate, with four columns A:D and five rows. Enter Years 1, 2, 3, 4 in A2:A5. Use cost 1600, salvage 100 and life 4.

The ordinary fixed-declining model has rate 1-(100/1600)^(1/4)=0.5. Enter =DB(1600,100,4,A2,12) in B2 and fill to B5. Independent model targets are 800, 400, 200, 100, leaving 800, 400, 200, 100 after the respective charges.

For a separate recurrence, put 1600 in C2 and =C2*0.5 in D2. Put =C2-D2 in C3 and =C3*0.5 in D3; fill C3:D3 through row 5. D reproduces the four charges without depending on a rounded approximate rate.

This is an independently derived model comparison with an exact 50% rate. It does not extend Apple’s short entry into a complete native specification for every possible cost/salvage relationship.

Use nonnegative cost and salvage, positive life and period, and a valid explicit month count. The reference does not enumerate all exact error labels, coercions or extreme-value outcomes. It documents period truncation, so a period of 2.9 uses period 2; it does not establish that arbitrarily distant periods are meaningful.

Keep asset amounts and useful-life assumptions separate from local accounting or tax rules. DDB uses a specified factor, VDB handles intervals and optional straight-line switching, and SLN is the direct straight-line calculation. A shared depreciation label does not make those methods interchangeable.