How to calculate the remaining balance on a loan
✓ Verified in LibreOffice 25.8.7.3How much you still owe after N payments — payoff planning, refinance math.
The formula
| App | Formula | Notes |
|---|---|---|
| Excel | =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. Every formula here is confirmed by actually executing it.