Last updated: 2026-05-09

The loan payment, defined

A loan payment is the fixed amount paid each period on a fully-amortizing, fixed-rate loan — the sum that, repeated for the whole term, exactly repays the borrowed principal plus all interest. Each payment is split between interest on the outstanding balance and a principal portion that reduces that balance, and the split shifts from interest-heavy to principal-heavy as the loan matures.

This calculator handles any fixed-rate, fully-amortizing loan with monthly compounding: auto loans, student loans, personal loans, business term loans. For mortgages — which add property tax, home insurance, and PMI to the monthly bill — see the dedicated Mortgage Payment Calculator.

How the math works

For a principal $L$, annual rate $r$, term $t$ in years (so $n = 12t$ months), the monthly payment is given by the standard PMT formula:

The remaining balance after $m$ months under an effective payment $\text{PMT}_\text{eff} = \text{PMT} + \text{extra}$ is

With an extra amount paid toward principal each month, the loan finishes early. The closed-form payoff month satisfies $B(n^\*) = 0$:

Both $B(m)$ and $n^\*$ assume the extra payment is applied to principal each month rather than held against future scheduled payments.

Worked example

Take a $25,000 auto loan at 7.5% annual interest over 5 years. The monthly rate is $r/12 = 0.075/12 = 0.00625$ and the term is $n = 60$ months. Substituting into the PMT formula gives a monthly payment of about $501. Over 60 months the borrower pays roughly $30,060 in total, of which about $5,060 is interest.

In the first month, interest is $0.00625 \times 25{,}000$ = $156.25, so only about $344 of that first $501 payment reduces the balance. By the final months the balance is small, interest is negligible, and almost the entire payment goes to principal.

Interest front-loading

Early in the loan the remaining balance is high, so the interest charge that month is high. Most of the scheduled payment covers interest, with only a small slice going to principal. As the balance shrinks, the interest charge shrinks with it, and more of each payment goes to principal — which accelerates the reduction. The amortization curve above shows this shift.

The same mechanism explains why an extra payment early in the loan removes more interest than the identical amount late: every dollar applied to principal eliminates the interest it would otherwise have accrued in every subsequent month.

Comparing offers with the scenarios view

The scenarios view holds several loan configurations side-by-side:

1. Set the inputs to offer A (rate, term, possibly an extra payment).
2. Save a snapshot — labelled, e.g., "6.9% / 60mo".
3. Change the inputs to offer B and save another snapshot.
4. Repeat for offer C.

The cards compare monthly payment, total interest, and the amortization curve side-by-side. Total interest is usually the most informative number when comparing loans of similar terms — a slightly lower monthly payment on a longer term often carries a higher lifetime cost.

Multi-currency

The calculator accepts USD, JPY, EUR, and GBP. The math is identical; the unit converter wraps the same closed-form computations. Switching currency allows a USD auto loan and a JPY auto loan to be compared side-by-side, which is useful for international audiences or for stress-testing a borrowing decision against currency volatility.

When extra payments are worth it

A common guideline: if the loan rate is higher than the after-tax return available elsewhere on the same dollars, prepaying reduces total cost. At 2026 rates this favors prepaying:

• Auto loans (typically 6–9% for prime borrowers)
• Most personal loans (typically 8–18%)
• Private student loans (typically 6–14%)

It generally does not favor prepaying:

• Federal subsidized student loans below 5% (especially with income-driven repayment in play)
• Long mortgages where the after-tax mortgage rate is below the expected retirement-account return — the comparison changes once retirement-savings contribution matching is counted as opportunity cost

This calculator gives the loan-side numbers; the Savings Goal Calculator gives the investment-side numbers, and the Compound Interest Calculator allows the two strategies to be compared.