Monthly payment,
on the first keystroke.

Field guide

How a monthly loan payment is calculated.

For any fixed-rate loan that fully amortizes, meaning the balance reaches zero on the last payment; every monthly payment is the same amount. That single number is what the calculator above solves for. The math is the standard amortization formula, the same one used by mortgage originators, auto-loan officers, and every personal-finance spreadsheet ever built:

L is the loan principal, n is the total number of monthly payments (years × 12 for a yearly term), and r is the per-month interest rate — the annual rate divided by twelve and by one hundred. So a 6% APR becomes r = 0.06 ÷ 12 = 0.005.

What the formula is doing, intuitively

The fixed payment must accomplish two things at once: pay down the principal so the balance hits zero, and cover the interest that accrues on the remaining balance every month. The formula above is the unique payment that satisfies both simultaneously. In any given month the split changes:

• Interest = current balance × monthly rate
• Principal = total payment − interest

On payment #1 the balance is the entire loan, so interest takes the biggest bite and principal the smallest. As the balance shrinks, interest shrinks with it and principal automatically grows by the same amount, since the total payment is constant. By the final payment, almost the entire amount goes to principal. (For the full month-by- month breakdown, see the Amortization Calculator.)

Worked example: $25,000 at 7.5% for 5 years

Using L = 25,000, r = 0.075 ÷ 12 ≈ 0.00625, n = 60:

Across 60 payments that's about $30,070 paid, of which $5,070 is interest, roughly 20% on top of the original loan.

The zero-rate edge case

When r = 0 the formula above is undefined (you'd divide by zero). The intuitive answer is also the right one: if there's no interest, the monthly payment is just the loan amount split evenly across the term: payment = L ÷ n. The calculator handles this case explicitly so a 0% promotional auto loan still produces a sensible number.

Why a slightly higher rate hurts more than you'd expect

The amortization formula is non-linear in r, which means doubling your rate doesn't double your payment; it grows it more than that, especially on long terms. A $300,000 30-year mortgage at 6% has a payment of about $1,799/mo. At 7% it jumps to ~$1,996/mo, an 11% bump in monthly payment for a 17% bump in rate. Over the full 360 payments, though, that 1-percentage-point difference adds about $71,000 in lifetime interest. Small rate differences, large dollar consequences.

Caveats

• Principal and interest only. This calculator outputs the loan's P&I payment. Mortgage payments typically also include escrowed property taxes, homeowners insurance, HOA dues, and (with low down payments) PMI; for a full housing payment, use the Mortgage Calculator.
• Fixed rate, fixed term. Adjustable-rate loans (ARMs), interest-only periods, and balloon structures change the math significantly. Use this for the standard fixed-rate case.
• End-of-period payments. The formula assumes payments are made at the end of each month (ordinary annuity convention, what virtually every consumer loan uses).
• APR vs note rate. Plug in the loan's note rate (the rate used to compute interest), not the APR (which includes mandatory fees). For most quoted consumer loans the two are identical.

Disclaimer

This calculator is an estimation tool. Final loan terms, fees, and qualifying rates depend on the lender, your credit profile, and the loan type. Always confirm the payment shown on your loan estimate or closing disclosure before signing.