How this instrument works
This is the balance a loan would carry after a specific number of payments at whatever amount was actually sent — not the amount a standard amortization table says should have been sent. Most balance tools work forward from an amortization schedule: they compute the exact payment that zeroes a loan out over its stated term, then read the balance off that schedule at any month. This one skips the schedule entirely. Feed it the starting principal, the rate, the real monthly figure, and a payment count, and it runs the arithmetic on those four numbers directly — which is the only way to answer the question when the payment on record does not match a textbook payment, because extra principal has gone in, a payment was smaller than the minimum, or the original loan documents are incomplete.
The shape of the formula follows from what a payment does to a growing balance. Left alone, a debt of P compounds to P(1+r)^k after k months at monthly rate r — the same growth an untouched deposit would earn. Each payment interrupts that growth by an amount that itself would have compounded had it been left to earn interest instead, so the k payments net out to PMT times the future-value-of-an-annuity factor, ((1+r)^k − 1)/r, and subtracting that factor from the compounded principal leaves whatever is actually still owed.
The result assumes every one of the k payments landed on time at the exact figure entered and that the rate held steady across all of them. A missed month, a skipped payment, or a rate reset on an adjustable loan will pull the true balance away from this estimate, higher if a payment was skipped and lower if extra ever went in beyond what was entered. It also excludes escrow, late fees, and the per-diem interest a lender tacks onto an official payoff quote for the exact day funds arrive, so treat the figure here as a close projection to check a statement against, not the cents-exact number to wire a payoff for.
- Enter the loan's starting principal under Original loan balance, $ — the amount financed at origination.
- Set the loan's rate under Annual interest rate, % — the figure on the note, not a blended or promotional rate.
- Enter the real figure sent each month under Actual monthly payment made, even if it differs from the lender's stated minimum.
- Enter the count under Payments made so far — how many of those payments have gone out to date.
- Read Remaining balance for the projected payoff after that many payments at that amount.
Worked example — five years of $1,500 payments on $250,000
Borrow $250,000 at a 6% annual rate and send $1,500 a month for five years — 60 payments. The monthly rate is r = 6 ÷ 1200 = 0.005, and sixty months of that compounding turns the growth factor (1.005)^60 into roughly 1.34885. Plugging in: B = 250000 × 1.34885 − 1500 × ((1.34885 − 1) ÷ 0.005), which comes to $232,557.49, the exact figure Remaining balance returns for these inputs — notice it is well above half the original principal, since most of each early $1,500 payment was still covering interest.
Change nothing but the payment: send $2,000 a month instead of $1,500 for the same 60 months and the balance drops to $197,672.48 — roughly $34,885 lower, all of it from the extra $500 landing on principal each month rather than sitting in the lender's pocket as interest. Set Payments made so far to zero and the formula returns the original $250,000 untouched, the sanity check that nothing has amortized yet.
Questions
Why doesn't this match my lender's official payoff quote?
A real payoff statement adds per-diem interest for the exact day the funds are received and any payoff-processing fee, and it reflects payments precisely as the servicer posted them, including timing quirks this formula cannot see. Treat this figure as a close projection to check a statement against, not a substitute for requesting the actual payoff letter before closing.
What if I have been paying more than the minimum?
Enter the real amount sent under Actual monthly payment made, not the lender's stated minimum — the formula credits every extra dollar toward principal exactly like the example above, where raising the payment from $1,500 to $2,000 across 60 months cut the remaining balance by about $34,885.
Can Payments made so far be zero?
Yes — entering zero returns the original balance unchanged, since no payment has yet offset the interest accruing on it. It is a useful check that the other fields are wired correctly before trusting a nonzero result.
Why would the remaining balance come out negative?
A negative figure means the entered payment, sustained for that many months, would have fully retired the loan before the payment count you entered — the loan paid itself off earlier, and the negative number is the excess beyond zero rather than debt still owed. Lower Payments made so far and rerun it to find roughly where the balance actually crosses zero.
How is this different from a standard amortization calculator?
A standard amortization calculator computes the exact payment that zeroes a loan out over its stated term, then reads the balance off that built-in schedule. This instrument takes the payment as a given instead of computing it, which is what a loan needs once real payments — extra principal, a shortfall, an odd one-off amount — have stopped matching any textbook schedule.
References
- Consumer Financial Protection Bureau — Mortgage servicing and payoff statements
- Federal Reserve — Consumer Credit statistical release (G.19)
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.