How to calculate the remaining balance on a loan

✓ Verified in LibreOffice 25.8.7.3 ✓ Verified in Google Sheets (2026-08-30)

How much you still owe after N payments — payoff planning, refinance math.

The formula

App	Formula	Notes
Excel (desktop)	`=FV(A2/12,D2,PMT(A2/12,B2*12,C2),C2)`	A2=rate, B2=years, C2=principal, D2=payments made. FV of the loan under its own payment stream.
Google Sheets	`=FV(A2/12,D2,PMT(A2/12,B2*12,C2),C2)`	Identical.
LibreOffice Calc	`=FV(A2/12,D2,PMT(A2/12,B2*12,C2),C2)`	Identical.

How it works

A loan balance is just a future value: the principal growing at the loan rate while the payment stream chips away at it. Nesting PMT inside FV keeps everything consistent — and the verification exploits that: after all 360 payments the balance must be exactly $0.00, which the engines confirm. Plug any smaller payment count into the periods argument for the balance at that point (after 60 payments of the $300k example: ~$279,163). Signs work out because PMT returns a negative payment against a positive principal.

Verified, not just documented

We ran =ROUND(FV(A2/12,B2*12,PMT(A2/12,B2*12,C2),C2),2) in LibreOffice 25.8.7.3 (headless, with forced recalculation) and it returned 0 — exactly the expected result. We then ran the same formulas in Google Sheets, executed 2026-08-30: a formula-only workbook goes into Google Drive, which converts it to a Sheet and recalculates every formula with Google’s own engine, and comes back out as .xlsx carrying the values Google computed. It returned 0 for the worked example, the same value LibreOffice produced. Both engines’ numbers on this page are executed results. The Excel formula follows Microsoft’s official documented syntax — we do not run desktop Excel.

Functions used

FV · PMT — see full Excel, Google Sheets & LibreOffice compatibility for each.

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IPMT vs PPMT: where each payment actually goes