Payment Calculator
Solve for monthly payment, loan amount, loan term, or interest rate — enter any three, get the fourth
What Is a Payment Calculator?
A payment calculator figures out one unknown value in a loan — the monthly payment, the loan amount, the loan term, or the interest rate — as long as you know the other three. Most calculators only work in one direction (given amount, rate, and term, find the payment), but this one solves in all four directions using the same amortization math, just rearranged for whichever variable you need.
How to Use It
- Choose what you want to solve for: Monthly Payment, Loan Amount, Loan Term, or Interest Rate.
- The field for that value disappears — fill in the remaining three fields.
- Click Calculate to see your answer, plus the full amortization schedule and charts.
- Use Copy, Print, or Share to save or send your results.
The Formulas Behind Each Mode
Solve for Payment: M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]
Solve for Loan Amount: P = M × [(1+r)ⁿ − 1] ÷ [r(1+r)ⁿ]
Solve for Loan Term: n = ln[M ÷ (M − P×r)] ÷ ln(1+r)
Solve for Interest Rate: No closed-form formula exists — solved numerically (bisection method) for the rate r that makes the payment formula above true.
In every formula, M = monthly payment, P = loan amount, r = monthly interest rate (annual ÷ 12), and n = number of monthly payments.
When to Use Each Mode
Solve for Payment
You know what you want to borrow and the rate/term — find out what you'll actually pay each month.
Solve for Loan Amount
You know your budget (monthly payment) — find out the maximum you can borrow at a given rate and term.
Solve for Loan Term
You know the loan and what you plan to pay each month — find out how long it will take to pay off.
Solve for Interest Rate
You know the loan, term, and payment — reverse-engineer the effective interest rate being charged.
Explanation of Every Input
Loan Amount
The total amount borrowed (or currently owed) before any payments are applied.
Annual Interest Rate
The yearly rate charged by the lender, automatically converted to a monthly rate for the underlying calculation.
Loan Term
The number of months over which the loan is scheduled to be fully repaid.
Monthly Payment
The fixed amount paid each month toward the loan, covering both interest and principal.
Advantages of Using This Calculator
- Solves for any of the four core loan variables, not just payment.
- Includes a full amortization schedule and charts once all values are known.
- Uses precise numerical methods for interest rate, matching spreadsheet/financial-calculator accuracy.
- Works for any fixed-rate, fully-amortizing loan type.
Limitations
- Assumes a fixed interest rate and fixed monthly payment throughout the term.
- Does not include taxes, insurance, or loan-specific fees — see the Mortgage or Auto Loan calculators for those.
- "Solve for Term" and "Solve for Rate" require a payment large enough to actually pay off the loan; otherwise no solution exists.
Common Mistakes to Avoid
- Entering a payment too low to cover even the interest, which makes Term/Rate unsolvable.
- Forgetting the rate field expects an annual rate, not a monthly one.
- Assuming "Solve for Rate" gives an APR that includes fees — it only reflects the base interest rate implied by the numbers entered.
Worked Examples
Solve for Payment
Input: Loan Amount $20,000, Rate 7%, Term 60 months
Result: Monthly Payment ≈ $396.02
The most common mode — three known values give you the fourth: what you'll actually pay each month.
Solve for Loan Amount
Input: Payment $400, Rate 7%, Term 60 months
Result: Loan Amount ≈ $20,202
Useful for figuring out how much you can borrow if you already know your budget and expected rate/term.
Solve for Loan Term
Input: Loan Amount $20,000, Rate 7%, Payment $500
Result: Term ≈ 44.6 months
Shows how quickly a higher-than-minimum payment could pay off the same loan amount.
Solve for Interest Rate
Input: Loan Amount $20,000, Term 60 months, Payment $396.02
Result: Interest Rate ≈ 7.0%
Reverses the payment example above — useful for checking what rate a known payment actually implies.
Frequently Asked Questions
What makes this different from a normal loan calculator?
Most loan calculators only solve for the monthly payment. This one can solve for any of the four core loan variables — monthly payment, loan amount, loan term, or interest rate — as long as you provide the other three, using the same underlying amortization math in every direction.
How do I calculate the loan amount I can afford from a target payment?
Select "Loan Amount" under Solve For, then enter the monthly payment you can afford along with your expected interest rate and loan term — the calculator works backward using the present-value form of the amortization formula to tell you the maximum loan amount that fits.
How do I find out how long it will take to pay off a loan at a fixed payment?
Select "Loan Term" under Solve For, then enter the loan amount, interest rate, and the fixed payment you plan to make — the calculator solves for the number of months needed to bring the balance to zero at that payment level.
Can this calculator tell me what interest rate I'm actually paying?
Yes — select "Interest Rate" under Solve For and enter the loan amount, term, and your known monthly payment; the calculator uses an iterative numerical method to find the rate that produces exactly that payment, which is useful for checking a lender's stated rate or an old loan's effective rate.
Why did I get an error when solving for loan term?
This happens when your entered payment is too low to ever pay off the loan at that interest rate — if the payment doesn't exceed the interest accruing each period, the balance would never shrink, so no finite term exists at those numbers.
Why did I get an error when solving for interest rate?
This means your payment is too low to pay off the loan amount within the given term even at a 0% interest rate — try a smaller loan amount, a longer term, or a higher payment.
What formula does this calculator use?
All four modes are built on the standard fixed-payment amortization formula, M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1], algebraically rearranged (or, for interest rate, solved numerically) depending on which variable you're solving for.
Does this work for any type of loan?
Yes — the underlying math applies to any fixed-rate, fully-amortizing loan, including personal loans, auto loans, mortgages, and student loans. For mortgage- or auto-specific extras like taxes, PMI, or trade-ins, use the dedicated Mortgage or Auto Loan calculators instead.
How accurate is the "solve for interest rate" result?
It uses a numerical bisection method that converges to a highly precise answer (well beyond typical decimal precision needed), so the result is effectively exact for practical purposes, matching what you'd get from a financial calculator or spreadsheet.
Can I see the full amortization schedule after solving?
Yes — once all four values are known (either entered or solved), the calculator displays the complete month-by-month and year-by-year amortization schedule along with principal-vs-interest and balance charts.
What is the difference between loan term and amortization period?
For most personal, auto, and standard loans they're the same — the loan is fully paid off by the end of the stated term. Some mortgages use a longer amortization period than the actual loan term (common in certain countries), which this calculator doesn't model separately.
Conclusion
Whether you're budgeting for a new loan, checking how fast extra payments could pay one off, or verifying the real interest rate behind a payment you already know, this calculator handles all four directions of the same core loan math in one place.