One formula, every fixed-payment loan
Mortgages, auto loans, student loans, personal loans — they all use the same equation to figure out your monthly payment. The Payment Calculator runs that equation. You give it any two of the three variables (loan amount, rate, term) and it solves for the third.
Most loan calculators are locked into one direction: enter loan amount, rate, and term, get a payment. The Payment Calculator does that, but it also runs in reverse. Tell it the monthly payment you can afford and it tells you the largest loan that fits. Tell it the payment and the loan and it tells you how long the payoff will take. Three calculators in one widget, no signup, results update as you type.
You don't need this calculator for every loan question. A mortgage shopping trip will give you payment quotes directly. But for the moments when you want to test "what if I borrowed $5,000 less?" or "what if I stretch this auto loan from 4 years to 6?" — and you want the answer in three seconds, not after a sales call — this is the tool.
How to use the Payment Calculator
Pick what you want to solve for, then fill in the other two.
- Choose the solve mode:
- Monthly payment — the standard direction. "What's my payment on a $25,000 auto loan at 7.5% for 5 years?"
- Max loan amount — work backward from a target payment. "If I can afford $500 a month at 7.5% for 5 years, what's the biggest loan I should take?"
- Payoff time — given a payment and a balance. "If I send $300 a month against a $10,000 balance at 7.5%, how long until I'm out of debt?"
- Enter the two known values. The unknown field disappears from the form. The remaining fields are the ones the calculator needs.
- Enter the rate as an APR. For US loans this is the rate the lender quotes — already annualized. The calculator divides by 12 internally for the monthly figure.
- Read the result. The headline is your unknown. Below it, you get total amount paid over the life of the loan and total interest as separate numbers. The split is usually informative.
The payoff date assumes you start the loan this month. If the loan starts later, just shift the payoff date by the same amount. The math doesn't change.
The formula, three ways
The base equation — what every amortization schedule starts from — solves for the monthly payment.
PMT = P × [r(1 + r)^n] / [(1 + r)^n − 1]
P = loan principal. r = monthly interest rate (APR ÷ 12 ÷ 100). n = total number of months. PMT = constant monthly payment.
This is the formula in your spreadsheet's PMT function and on the back of every loan officer's calculator. It assumes the loan amortizes — every monthly payment is the same dollar amount, the loan pays off completely at the end of the term, and interest is calculated each month on the remaining balance.
Algebra lets you rearrange the same equation to solve for either of the other variables. Solving for P (the maximum loan you can take given a target payment):
P = PMT × [(1 + r)^n − 1] / [r(1 + r)^n]
Solving for n (months to pay off given a loan and a payment):
n = ln(PMT / (PMT − P × r)) / ln(1 + r)
The Payment Calculator switches between these three forms when you change the solve mode. Same formula, three faces.
A worked example: $25,000 auto loan at 7.5% for 5 years
You're shopping for a used car. The dealer offers $25,000 financed at 7.5% APR over 5 years. Let's run the math.
P = $25,000, APR = 7.5%, so r = 0.075 ÷ 12 = 0.00625. Term = 5 years = 60 months, so n = 60.
Plug into the PMT formula:
- (1 + 0.00625)^60 ≈ 1.4540
- Numerator: 0.00625 × 1.4540 ≈ 0.009088
- Denominator: 1.4540 − 1 = 0.4540
- PMT = 25,000 × 0.009088 / 0.4540 ≈ $500.42 per month
Over 5 years you'll pay 60 × $500.42 = $30,025. Of that, $25,000 is the original loan and the remaining $5,025 is interest. Twenty percent of the original loan, paid as a fee to the lender over five years.
Now flip the question. Say your budget caps out at $400 a month for an auto payment, same rate and term. How much car can you afford? Solve for P:
- P = 400 × [(1.00625)^60 − 1] / [0.00625 × (1.00625)^60]
- P = 400 × 0.4540 / (0.00625 × 1.4540)
- P = 400 × 0.4540 / 0.009088
- P ≈ $19,987
So $400 a month buys you about $20,000 of car at that rate. The difference between $400 and $500 a month is roughly $5,000 of borrowing capacity — a useful number to know before you walk into a dealership.
Payment scales with rate, but not linearly
People sometimes assume a 1% rate increase means a 1% payment increase. Not even close. The payment formula puts the rate in the exponent, so changes compound across the term. The longer the loan, the more dramatic the effect of rate changes.
Here's how a fixed $300,000 30-year mortgage payment shifts as the rate moves:
| Interest rate | Monthly P&I | Total paid (30 yrs) | Total interest |
|---|---|---|---|
| 4.0% | $1,432.25 | $515,609 | $215,609 |
| 5.0% | $1,610.46 | $579,767 | $279,767 |
| 6.0% | $1,798.65 | $647,514 | $347,514 |
| 7.0% | $1,995.91 | $718,528 | $418,528 |
| 8.0% | $2,201.29 | $792,464 | $492,464 |
Going from 4% to 8% — a 4-point increase — nearly doubles the total interest paid over the loan's life. The monthly payment "only" goes up by about 54%, but the long-term cost difference is $276,855. This is why rate shopping matters more than rate-shopping articles tend to convey.
What this calculator does not cover
The Payment Calculator solves the principal-and-interest math. Real loan payments often include other things bundled in.
- Mortgage escrows — property tax, homeowner's insurance, and PMI (if you put less than 20% down) typically ride along in your monthly mortgage payment. The lender holds them in escrow and pays them on your behalf. PITI ("principal, interest, taxes, insurance") is the full mortgage payment; the Payment Calculator gives you just the PI.
- Auto loan add-ons — extended warranty, gap insurance, sales tax that's been financed into the loan. These can push the actual financed amount above the sticker price, which changes the payment.
- Origination fees and points — sometimes folded into the loan amount, sometimes paid up front. APR accounts for fees in the rate; the bare interest rate doesn't.
- Variable-rate loans — the calculator assumes a fixed rate for the full term. If your loan is an ARM or has a teaser rate that resets, the schedule changes when the rate changes.
For mortgages with full PITI, use a dedicated mortgage calculator. For everything else, the Payment Calculator's numbers are essentially what shows up on the loan itself.
Some loans don't fit this formula at all
The PMT formula works for amortizing loans. A few common money problems aren't amortizing and need different math.
- Credit cards. No fixed term, no fixed payment, interest compounds daily on a balance that changes when you spend or pay. The minimum payment is a percentage of the balance, not a constant. There's no PMT formula for credit card payoff.
- Simple-interest loans. Interest is calculated only on the original principal, not on the running balance. Some short-term personal loans and a handful of car loans work this way. For these, the Simple Interest Calculator is the right tool.
- Interest-only loans. You pay only interest for a fixed period, then either refinance, pay a balloon, or start amortizing. The Payment Calculator can model the amortizing phase, but the interest-only phase is a flat (P × r) calculation per month.
- Income-driven student loan plans. Federal income-driven repayment plans recalculate the payment based on income, not principal. The PMT formula doesn't apply during the income-driven phase.
Other Microapp tools that pair with this one
- Amortization Calculator — same formula, but produces the full month-by-month schedule showing exactly how interest and principal split each month.
- Mortgage Payoff Calculator — adds extra monthly payments to the amortization and reports how many months and how much interest you save.
- Simple Interest Calculator — the non-amortizing alternative for loans that charge interest on the original principal only.
- Savings Calculator — same compounding math in your favor. Useful when comparing extra debt payments against putting the money in a high-yield savings account.
- Salary to Hourly — context for "can I afford this payment" decisions. Useful when sizing what a monthly figure represents in hours of work.
Frequently asked questions
What's the difference between APR and interest rate?
For an amortizing loan, the APR is essentially the interest rate plus any fees expressed as an annualized cost. With zero fees, APR equals the rate. With fees (origination, discount points, processing), the APR is slightly higher than the bare rate. Federal regulations require lenders to disclose APR for comparison shopping. Enter the APR for the most realistic payment calculation. For auto and personal loans, "APR" is usually what's quoted anyway.
What loans does this work for?
Any amortizing loan with a fixed monthly payment and a fixed term. That covers most mortgages, auto loans, personal loans, and many student loans. It does not work for credit cards (revolving credit, no fixed term), interest-only loans, balloon loans, or simple-interest loans (use the Simple Interest Calculator for those).
Why is total interest so much higher than the loan amount on long loans?
Because interest compounds across a long time horizon. A $25,000 5-year auto loan at 7.5% has total interest of about $5,000 — 20% of the principal. A $300,000 30-year mortgage at 7% has total interest of about $418,500 — 140% of the principal. Same rate, very different total cost, because the mortgage runs six times longer. This is why shorter loan terms save big money in absolute dollars even though they raise the monthly payment.
How accurate is this versus my lender's quote?
Within a few cents on the principal-and-interest portion. Lenders use slightly different rounding conventions and may include escrow items in the figure they quote you. The Payment Calculator gives pure PI. If your lender's monthly figure is much higher than what the calculator shows for the same loan, the difference is almost always property tax, insurance, or PMI bundled into the lender's number.
Can I model extra payments in this calculator?
Not here — the Payment Calculator runs the basic PMT formula. For extra-payment scenarios, use the Mortgage Payoff Calculator. It runs both the regular schedule and the accelerated schedule side by side and reports months saved and interest saved.
What if my monthly payment is too low to pay off the loan?
If the payment is less than the monthly interest on the principal, the loan grows instead of shrinks — called negative amortization. In real life, lenders won't structure a normal loan this way; the minimum payment is set to at least cover interest. The Payment Calculator detects the impossible case in payoff-time mode and returns an error instead of an infinite loop. If you see it, try a higher payment.
Why does the payoff time show years AND months?
Because the answer rarely lands on a clean year boundary unless the term happens to be a whole-year multiple. A 5-year auto loan is exactly 60 months. But if you're solving for payoff time given a custom monthly payment, the answer might be 47.3 months — 3 years, 11 months, and change. The display rounds months to the nearest whole number; the underlying math uses the exact decimal.
Does this work for international loans?
The formula is universal, but loan conventions differ between countries. UK mortgages often use slightly different interest calculation methods. Some European loans pay quarterly or biannually instead of monthly. For US-style monthly amortization, the calculator is exact. For other conventions, the result will be a close approximation, not penny-perfect with your local lender's quote.