Apple Numbers PPMT: Principal Repayments and Remaining Loan Balance

• Introduced: The original introduction release and date are not established by the checked sources.
• Availability: Currently documented in Apple’s Functions Help 15.4 documentation edition; no final supported-version endpoint is established.
• Scope: Shared iWork reference. Exact historical availability in individual Mac, iPad, iPhone and iCloud builds remains unverified.
• Checked: October 14, 2026, against the official PPMT reference. Documentation and independent payment schedules; no native Numbers test.

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

The first four arguments are required: rate per payment period, payment number, total number of periods and initial value. Period must be greater than zero; Apple’s entry lists num-periods as at least zero. The examples use positive whole-number terms and payment numbers within the term, avoiding degenerate or out-of-range cases whose outcomes are not fully specified.

Future-value is optional and defaults to 0. When-due is optional: 0 or omitted means end-of-period payments; 1 means beginning-of-period payments. The rate and period count must use the same time unit. Use 6%/12 for a nominal annual rate of 6% with monthly periods, rather than entering 6% as the monthly rate.

A loan received initially is a positive present value; repayments are negative cash flows. A remaining balloon liability is entered as a negative future value. Currency formatting follows regional settings but does not change these signs or the timing model.

Create a Numbers table named PrincipalParts, with seven columns A:G and four rows including one header row. Put Period, Principal, Interest, Total payment, Parts sum, Opening balance and Closing balance in A1:G1. Enter 1, 2, 3 in A2:A4.

Enter =PPMT(10%,A2,3,331,0,0) in B2, =IPMT(10%,A2,3,331,0,0) in C2, =PMT(10%,3,331,0,0) in D2 and =B2+C2 in E2. Fill B2:E2 through row 4.

Put 331 in F2 and =F2+B2 in G2. Enter =G2 in F3 and =F3+B3 in G3, then fill F3:G3 through row 4.

The principal amounts total -331, exactly repaying the original principal in the model. Subtracting the full 133.1 from the balance each period would also subtract interest as if it were principal and produce the wrong balance.

For a separate sum control, create a two-column table named Totals, with four rows. Enter =-100-110-121 in B2, =-33.1-23.1-12.1 in B3 and =-133.1*3 in B4. Expected totals are -331, -68.3 and -399.3. Principal plus interest equals total cash paid.

On a separate table named DueAtStart, with three columns and four rows, enter periods 1–3 in A2:A4. Put =PPMT(10%,A2,3,331,0,1) in B2 and =IPMT(10%,A2,3,331,0,1) in C2; fill B2:C2 through row 4.

Expected principal amounts are -121, -100, -110; interest amounts are 0, -21, -11. Every beginning-of-period payment totals -121. The first immediate payment is entirely principal in this independent model.

Both timing models repay 331 of principal, but their interest totals differ: -32 at the beginning versus -68.3 at the end. Do not change the timing argument in one component while leaving the PMT or other component on a different schedule.

Create another table named BalloonPrincipal, with five columns A:E and 121 rows, including a header row. Put Period, Principal, Interest, Payment and Remaining balance in A1:E1. Enter 1 in A2 and =A2+1 in A3; fill A3 through A121.

Enter these formulas in row 2 and fill B2:D2 through row 121:

• B2: =PPMT(6%/12,A2,120,200000,-100000,0)
• C2: =IPMT(6%/12,A2,120,200000,-100000,0)
• D2: =PMT(6%/12,120,200000,-100000,0)

In E2 enter =200000+B2, then =E2+B3 in E3 and fill to E121. Selected independent results are:

Each payment is approximately -1610.205019416. Apple explicitly publishes period 25’s principal, interest and payment to two decimals; the remaining balance and full schedule are independent calculations.

The 120 regular principal reductions total -100000, leaving the other 100000 for the specified balloon. A remaining balance of 100000 is therefore expected, not an amortization error. Keep the balloon separate from the regular payment components.

The short reference does not establish every exact error token, fractional payment-number behavior or degenerate term result. Keep the model’s rate, term, future value and timing consistent in every component. Use actual numeric inputs, and retain precision through balance recurrences.

This fixed-payment model does not choose a lending policy or include unentered fees, prepayments or irregular accrual conventions. A statement may differ because its cash flows or rounding policy differ from the mathematical assumptions here.

IPMT gives the interest portion; PMT gives the payment. CUMPRINC adds principal portions over an interval but does not accept a future-value argument for the balloon example.