Fixed monthly payment for any loan.
M = P × [r(1 + r)^n] / [(1 + r)^n − 1]
The standard fixed-payment loan formula is derived from the present-value annuity equation. It calculates the constant periodic payment M that, when paid every period, exactly pays off the loan principal plus accrued interest by the final payment. This formula applies to fully amortizing, fixed-rate loans — the most common type for mortgages, auto loans, and personal loans.
M = 25,000 × [0.005 × (1.005)^48] / [(1.005)^48 − 1] (1.005)^48 = 1.27049 (rounded) Numerator: 0.005 × 1.27049 = 0.0063524 Denominator: 1.27049 − 1 = 0.27049 M = 25,000 × (0.0063524 / 0.27049) M = 25,000 × 0.023485 M ≈ 587.13
Result: Monthly payment ≈ **$587.13**
A $25,000 auto loan at 6% annual interest over 4 years requires a fixed monthly payment of approximately $587.13. Over the life of the loan you pay 48 × $587.13 = $28,182.24 in total, meaning $3,182.24 goes to interest. Early payments are interest-heavy; later payments chip away more principal — that is the nature of amortization. Results are estimates. Your actual payment may differ based on origination fees, rounding conventions, or lender-specific terms.
Amortization means spreading a loan's repayment across equal periodic payments. Each payment covers the interest that accrued during that period, with the remainder reducing the principal balance. Because the balance shrinks over time, the interest portion of each payment falls while the principal portion rises — even though the total payment stays constant.
A higher interest rate raises the monthly payment and dramatically increases total interest paid. On a $300,000 30-year mortgage:
That 3-percentage-point difference costs over $200,000 in extra interest over the loan's life.
The calculated monthly payment covers principal and interest only. For mortgages, your total monthly housing cost typically also includes:
Always budget for these additional costs.
This calculator uses a fixed interest rate, which keeps M constant for the entire term. Adjustable-rate mortgages (ARMs) start with a fixed period, then reset periodically — so the payment can change. Recalculate with the new rate whenever an ARM adjusts.
Making even one extra payment per year, or rounding up your monthly payment, can shorten the loan term significantly and save thousands in interest. For example, paying an extra $100/month on a $200,000 30-year mortgage at 6% can cut the term by about 4 years and save over $27,000 in interest.
Loan payment results from this calculator are estimates for educational purposes only. Actual payments may differ based on lender fees, compounding conventions, insurance, taxes, and other factors. Consult your lender or a licensed financial advisor before making borrowing decisions.
Financial advisors generally recommend that total car expenses (payment + insurance + fuel) stay below 15–20% of your take-home pay. Use the calculator to find a payment that fits within that budget by adjusting the loan amount or term.
At 7% interest over 30 years: M = 200,000 × [0.005833 × (1.005833)^360] / [(1.005833)^360 − 1] ≈ **$1,331/month** for principal and interest. Taxes, insurance, and PMI are additional.
Yes — a longer term spreads the same principal over more payments, reducing each payment. However, you pay significantly more total interest. A 60-month auto loan at 6% has a lower monthly payment than a 36-month loan, but you pay more interest overall.
Credit score affects the interest rate a lender offers you. A higher score typically qualifies you for a lower rate, which directly lowers your monthly payment and total interest cost. Even a 1% rate difference on a 30-year mortgage can mean tens of thousands of dollars.
Every amortizing payment splits into two parts: the **interest** (the cost of borrowing for that period, calculated as r × remaining balance) and the **principal** (the remainder, which reduces what you owe). Early payments are mostly interest; later payments are mostly principal.
You need three inputs: (1) the loan principal (amount borrowed), (2) the annual interest rate, and (3) the loan term in years or months. All other variables are derived from these.
Yes. The amortization formula is the same for any fixed-rate, fully amortizing installment loan — mortgage, auto, student, or personal. Just enter the correct principal, rate, and term for your specific loan.
The formula calculates principal and interest only. Your mortgage servicer typically collects property taxes and homeowner's insurance in escrow, and possibly PMI, which are added on top of the P&I payment.
Multiply your monthly payment M by the total number of payments n to get the total amount paid. Subtract the original principal P to get total interest: Total Interest = (M × n) − P.
A larger down payment reduces the principal P. Since M is directly proportional to P, a smaller loan balance means a lower monthly payment and less total interest paid over the life of the loan.
Yes, but adjust the inputs. For bi-weekly payments, divide the annual rate by 26 to get r, and multiply the term in years by 26 to get n. Note that 26 bi-weekly payments per year differs from 24 semi-monthly payments.
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