PMT Function in Apple Numbers: Syntax, Examples and Troubleshooting

• Introduced: Documented in Apple’s Formulas and Functions Help 15.4; the first release is not established.
• Availability: Currently documented for Numbers in that help version; 15.4 is not a final supported-version endpoint.
• Scope: Shared iWork function help; older-release and individual-client availability are not established by this check. Currency display follows Language & Region settings.
• Checked: October 14, 2026, against the official PMT reference. Documentation and independent arithmetic checks; no native Numbers test.

PMT determines the same payment amount each period required to connect an initial balance, a final balance, a fixed periodic interest rate, and a fixed number of periods. It is useful for amortizing loans, balloon loans, leases and regular-payment annuities. It does not calculate the total price of a loan after separate insurance, property taxes, fees or an adjustable-rate reset. For irregular or varying cash flows, build a different model. Apple specifically groups PMT with PV, FV, NPER and RATE for regular cash flows.

=PMT(periodic-rate, num-periods, present-value, future-value, when-due)

Apple shows optional arguments inside its function definition and explains the 0/1 payment timing; do not reverse the sign of only one loan component without checking the cash-flow perspective. The documented allowance of num-periods=0 does not guarantee a finite payment in that case: with zero payment periods, the payment calculation can be undefined. For repayment examples use a strictly positive number of periods.

Finance math behind the result

For rate r, number of periods n, starting balance PV, signed ending cash value FV, and timing flag t, the independently checked conventional fixed-rate cash-flow relationship is:

q = (1 + r)^n
factor = ((q - 1)/r) * (1 + r*t)       for r ≠ 0
payment = -(FV + PV*q)/factor

At a zero interest rate, the simplified model for positive n is payment = -(FV + PV)/n. This algebra explains expected outputs; Apple’s help does not promise a particular internal numerical algorithm or error message.

Create a single table named Loan with two columns A: Input and B: Value. Give it at least twelve rows. Enter these actual numbers in the B cells, without a $ text prefix. Enter formulas in the destination cells indicated—not in cells used as inputs.

Expected outputs, rounded for currency display: B8 = -1,610.21, B9 = -2,220.41, B10 = -1,432.86, B11 = -2,209.36, and B12 = +1,610.21. Apple’s reference publishes the first three expected PMT results; the beginning-of-period comparison is independently calculated.

The balloon loan has a smaller periodic payment because $100,000 remains due at maturity: that does not make its overall financing obligation simply cheaper. To compare alternatives, account for the balloon, any fees and the same time horizon. Never strip the negative sign from a financial formula before using it as a cash-flow input.

Table references and input precision

If calculating from a second table, Numbers may generate Loan::B2 for a reference to this table; a different sheet can require a qualifier like Budget::Loan::B2. Refer to Apple’s table-reference guidance and select actual cells rather than typing Excel Budget!B2 notation. Keep rates as numeric 0.06 or 6%, not as a text value "6%".

1. Zero-rate repayment: =PMT(0,24,12000,0,0) has an independently calculated result -500.00. There is no interest, so 24 payments of $500 exactly offset the $12,000 originally received.

2. Small-loan budgeting: =PMT(0.05/12,36,12000,0,0) gives approximately -359.65. For a positive nominal total, enter =-PMT(0.05/12,36,12000,0,0)*36; the expected result is 12947.43, before separate fees. This uses the unrounded payment. Use =ROUND(PMT(0.05/12,36,12000,0,0),2) only when you need the underlying payment rounded to -359.65, rather than merely displaying two decimals.

3. Interest versus principal: Apple’s published 25th-payment comparison for the $200,000 balloon example shows IPMT approximately -922.41 and PPMT approximately -687.80, together -1,610.21. These two functions split the payment into its interest and principal components. For details consult the official Apple IPMT and Apple PPMT reference pages, whose destinations were checked against Apple’s current documentation on October 14, 2026.

Precision note: PMT usually returns a non-integer amount. Currency formatting may display cents while the cell holds more digits. Rounding every payment before amortization can create a small residual versus using the full precision, especially for long schedules. Apple’s PMT help does not resolve a lender’s specific contractual cents-rounding policy.

When exchanging a workbook, recheck payment timing, signs and separators in the receiving program.

• Apple PMT — exact syntax and examples (official, checked).
• Apple guidance: PV, FV, PMT, NPER and RATE (official, checked).
• ROUND tutorial in Apple Numbers.

Use commas between arguments in English-locale formulas. If your decimal separator is a comma, use semicolons between arguments. A cell-reference formula avoids decimal-literal ambiguity: =PMT(B2/B3;B4*B3;B5;B6;B7). Select source cells in the Numbers formula editor to insert the correct table and sheet qualifiers.

• Apple functions overview: argument notation and regional separators.
• Apple cell-reference guide: table names and cross-sheet references.

The examples illustrate a fixed-rate model. They do not include taxes, fees or a lender’s contractual rounding rules.