How this instrument works
Most loan calculators start from a term you already agreed to — 36 months, 60 months, 30 years — and solve for the payment that clears the balance by the end of it. This instrument runs that question in the other direction: it holds Desired monthly payment, $ fixed at whatever figure the borrower has actually decided to spend, then solves for the number of months that fixed payment takes to bring a loan of Loan amount, $ down to zero at Annual interest rate, %. Because interest keeps compounding on whatever balance survives each month, isolating the number of months requires a natural logarithm — there is no shortcut that skips it once the payment and rate are locked in.
The distinction matters most to someone who already knows their monthly budget and is shopping loan offers, or deciding whether to voluntarily pay more than a lender's stated installment on a personal loan, a debt-consolidation loan, or any other fixed-principal debt carrying a set rate. Two lenders quoting different rates on the same amount, tested at the identical target payment, resolve to two different payoff dates — that comparison, not the advertised rate alone, is what actually decides which offer finishes sooner.
The arithmetic assumes the rate and the payment both hold steady for every remaining month, with no skipped payments, no late fees, and no extra principal added outside the stated amount. It also requires the payment to exceed that first month's interest charge — Loan amount, $ multiplied by the monthly rate — or the balance never falls at all and the formula returns no real solution. This sheet reports the months a level payment takes; it says nothing about whether that payment fits comfortably alongside everything else a monthly budget competes with.
- Enter what you owe under Loan amount, $ — the loan's full remaining principal.
- Set the rate stated on the loan under Annual interest rate, % — the figure the lender quotes, not a teaser rate that has already expired.
- Enter the flat amount you plan to send every month under Desired monthly payment, $ — your own chosen figure, not a lender-set minimum.
- Read Months needed to pay off at that payment for the exact month the balance reaches zero if the payment never changes.
- Change Desired monthly payment, $ and rerun it to see how many months a higher or lower amount actually buys or costs.
Worked example — a $20,000 loan on a $500 monthly budget
Take the golden case: a $20,000 loan (Loan amount, $) at 8% annual interest (Annual interest rate, %), paid down at a fixed $500 every month (Desired monthly payment, $). The monthly rate is r = 8 ÷ 1200 = 0.0066667, and rL ⁄ PMT works out to 0.266667, so 1 minus that is 0.733333. Taking −ln(0.733333) gives 0.310155, and dividing by ln(1.0066667) = 0.0066445 returns n = 46.6781449734 — just over three years and ten and a half months of steady $500 payments before the balance reaches zero.
Raise that same $20,000 loan's payment to $1,000 a month and the identical formula returns 21.5365977313 months — barely half the time, because a heavier payment reaches past the fixed monthly interest and into principal far faster. Cut the loan itself in half instead, to $10,000, while leaving the payment at $500, and the answer comes back exactly the same 21.5365977313 months: what actually drives the payoff calendar is the ratio between the loan and the payment, not either figure alone.
Questions
Why can't I just divide the loan by the payment to get the months?
Because interest keeps accruing on whatever balance survives each month, so a simple division ignores how much of each payment actually retires principal. The formula rearranges the compounding identity and isolates months with a natural logarithm — the only way to solve for an exponent once the rate and payment are fixed. On the $20,000 example at 8% and $500 a month, naive division suggests 40 months; accounting for interest, the real answer is 46.6781449734.
What happens if my payment barely covers the interest?
The payoff time stretches out fast. On a $20,000 loan at 8%, the first month's interest alone is about $133.33 (Loan amount, $ times the monthly rate), so a $150 payment only sends about $16.67 of it toward principal that first month and returns roughly 330.7 months — over 27 years. Drop the payment to $133.33 or below and the balance stops falling altogether; the formula has no real solution at or under that floor.
Does the payoff time depend on the loan size, or just the payment?
Only on the ratio between them, together with the rate — not on either dollar figure alone. A $10,000 loan at 8% paid off at $500 a month takes 21.5365977313 months, the identical figure a $20,000 loan at the same rate returns once the payment is doubled to $1,000, because both pairs share a loan-to-payment ratio of 20. Scale the loan and the payment together and the payoff calendar does not move.
How is this different from a calculator that gives me my monthly payment?
That calculator fixes how many months you will pay and solves for the payment a lender would charge; this one fixes the payment you are willing to spend and solves for how many months that choice takes to clear the loan. It is the tool for comparing loan offers against a monthly budget you have already set, rather than shopping by a preset term like 36 or 60 months.
Does this assume the rate and payment stay exactly the same throughout?
Yes. Every month of the payoff uses the same rate and the same payment, with no late fees, no skipped months, and no extra principal added beyond the stated amount. A rate that resets, a payment that changes, or a lump sum paid down early all move the real payoff date — rerun the calculation with the new figures rather than adjusting this result by hand.
Who typically runs a payoff-time calculation like this?
Borrowers with a personal loan, a debt-consolidation loan, or another fixed-principal installment debt who already know what they can afford each month and want the payoff date that budget implies. It is also useful for comparing two lenders' rate quotes at the identical target payment, or for testing whether paying above a lender's stated installment meaningfully shortens the loan.
References
- Consumer Financial Protection Bureau — Consumer Tools for loans and credit
- 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.