How to use this calculator
- Choose what you want to solve for: the monthly payment (most common), the loan term, the interest rate, or the loan amount.
- Fill in the three known values. For example, to solve for the term, enter the loan amount, interest rate, and the payment you want to make.
- Add an origination fee, as a percentage or a flat dollar amount, if your lender charges one — the calculator shows the resulting APR alongside your interest rate.
- Pick the month your first payment is due so the schedule and payoff date line up with the calendar.
- Review your results, the balance and principal-vs-interest charts, and the full amortization schedule — export it to CSV or share the link.
How it's calculated
The standard fixed-rate amortization formula ties four things together: loan amount (L), monthly rate (r, the annual rate ÷ 12), number of payments (n), and payment (M): M = L × r(1 + r)n ÷ [(1 + r)n − 1]. Give the calculator any three and it solves for the fourth.
Solve for payment plugs your amount, rate, and term straight into the formula above. Solve for term finds the smallest whole number of monthly payments, at your fixed payment amount, that reaches a $0 balance (a payment at or below the first month's interest never pays it off). Solve for rate searches for the annual rate that makes your amount, term, and payment consistent, using bisection to 1/10,000 of a percent. Solve for amount finds the largest loan a given payment supports over the term at that rate.
APR is estimated the way lenders spread an origination fee over the loan: the fee is subtracted from the amount you actually receive, and the calculator solves for the rate that would produce your same payment on that smaller, fee-adjusted amount. A larger fee or a shorter term pushes the APR further above your quoted interest rate.
Each month, interest is the remaining balance times the monthly rate; the rest of the payment reduces principal. Calculations keep full precision month to month and round only the numbers you see, and the final payment is trimmed so the balance ends at exactly $0.
Every schedule is capped at 100 years of payments, so an input that can never be paid off (like a payment below the interest-only amount) is reported clearly instead of freezing the calculator.
Assumptions
- The interest rate is fixed for the entire term, with interest accruing monthly — adjustable-rate and interest-only loans aren't modeled.
- The origination fee is the only fee included in the APR estimate; other closing costs, discount points, or third-party fees a lender's official APR would include aren't captured.
- When you solve for the term (entering a payment and letting the calculator find how many months it takes), the APR estimate assumes that same level payment for every month, even though the true final payment in that scenario is usually a bit smaller (the last payment is trimmed to avoid overpaying). This overstates the APR by at most a few basis points — negligible for comparing offers, but worth knowing if you need the estimate to the exact basis point.
- There are no late fees, prepayment penalties, or skipped payments in the schedule.
- "Solve for term" and "solve for rate" assume a payment large enough to eventually retire the loan; if it isn't, the calculator tells you rather than guessing.
- Results are estimates for planning. Your lender's Loan Estimate or Truth in Lending disclosure shows your actual APR and terms.
Frequently asked questions
How do you calculate a loan payment?
Monthly payment uses M = L × r(1+r)^n ÷ [(1+r)^n − 1], where L is the loan amount, r is the annual rate divided by 12, and n is the number of monthly payments. A $20,000 loan at 7% for 4 years (48 months) comes to about $478.92 a month.
What's the difference between the interest rate and the APR?
The interest rate is what's applied to your balance each month to calculate interest. The APR (annual percentage rate) also factors in upfront fees like an origination fee or points, spreading their cost over the loan so you can compare offers with different fees on equal footing. The APR is always at or above the interest rate whenever there's a fee.
What does "solve for term" or "solve for rate" do?
Instead of always computing the payment from an amount, rate, and term, this calculator can hold any three of those four values fixed and solve for the missing one. For example, if you know the amount, rate, and the payment you can afford, "solve for term" tells you how many months it will take to pay it off.
Why did I get "this loan never pays off" for solve for term or rate?
That message appears when your chosen payment doesn't even cover the first month's interest on the loan amount — the balance would grow instead of shrink, no matter how many payments you made. Increase the payment, lower the rate, or reduce the loan amount to fix it.
How does an origination fee affect my APR?
An origination fee is deducted from what you actually receive, but your payment is still based on the full loan amount at the interest rate — so your effective borrowing cost, the APR, comes out higher than the interest rate. A 2% fee on a shorter-term loan raises the APR more than the same fee on a longer-term loan, because the fee is spread over fewer payments.
Should I compare loans by interest rate or APR?
Use the APR to compare loans with different fees, since it standardizes the fee's cost into a single rate. Use the interest rate to know exactly how your monthly payment and amortization schedule are calculated — that's what actually determines your payment, not the APR.
What loan term should I choose?
A shorter term means a higher monthly payment but far less total interest, since you're borrowing the money for less time. A longer term lowers the payment but costs more overall. Use "solve for payment" at a couple of different terms to compare the trade-off directly for your numbers.
Does this calculator work for personal loans, boat loans, or other fixed-rate loans?
Yes — the amortization math is the same for any fixed-rate, fixed-term loan with equal monthly payments. For a mortgage with taxes, insurance, and PMI, or an auto loan with trade-in and sales tax, use those dedicated calculators instead.
Can I pay off this loan early?
Yes — this calculator assumes level payments with no prepayment penalty. Making an extra payment reduces your balance immediately, which lowers every future month's interest, though you'd need to re-run the schedule with a shorter term or higher payment here to see the new payoff date, since ongoing extra payments aren't modeled on this calculator.
Why does my lender's payment differ slightly from this calculator's?
Small differences usually come from day-count conventions (some lenders charge interest based on the exact number of days in a month rather than a flat 1/12 of the annual rate), rounding rules, or fees your lender includes in the payment that aren't part of the amortization formula, like tacked-on insurance.
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Disclaimer: This calculator provides estimates for educational purposes only and is not financial, tax, or legal advice or an offer of credit. Actual payments depend on your lender, loan terms, taxes, and insurance. Consult a qualified professional before making financial decisions.