Loan Calculator

How to use this loan calculator

Pick what you want to work out, fill in the three fields you know, and read the answer. In the default Payment mode that is amount, rate and term. The other modes invert the same arithmetic: give a payment and get the amount you could borrow, the rate it implies, or how long it would take.

1. Amount, rate, term. Enter the rate on the note, not the APR — fees belong in Advanced options, where they are handled properly.
2. Payment frequency. Monthly by default; semi-monthly, biweekly, weekly, quarterly and annual are all modelled on their own cadence, not approximated from a monthly figure.
3. Advanced options, when they apply: compounding basis, start and first-payment dates, origination and fixed fees with their treatment, and the repayment structure.
4. Read the result panel, then the schedule, chart and milestones below it. Use What if? to preview a change before committing to it.

How loan payments are calculated

A fixed-rate instalment loan uses one formula. The payment is the amount financed divided by the annuity factor for the number of payments at the periodic rate:

M = P · r / (1 − (1 + r)⁻ⁿ)

• P — the amount financed: what you borrow, plus any fee you chose to finance.
• r — the periodic interest rate: the nominal annual rate converted to one payment period.
• n — the number of payments: the term expressed in payment periods.

The zero-rate branch. At r = 0 the formula divides by zero, so it is not used. A 0% loan repays M = P / n exactly, and this calculator returns exactly that — total interest of precisely zero, not a rounding artefact.

Worked example. $25,000 at 7.5% over 60 months: r = 7.5% ÷ 12 = 0.6250% a month, n = 60, so M = $500.95. Across the loan that is $5,056.92 of interest, or $202.28 for every $1,000 borrowed.

Load this example Puts these figures into the calculator above.

Understanding your loan results

Estimated payment

The level instalment. Every payment is this figure except the last, which is adjusted to clear the balance exactly.

Total interest

Every interest charge across the schedule. It is not a fee and not negotiable separately — it falls out of amount, rate and term.

Total cost

Total interest plus every fee. This is the number to compare offers on.

Estimated APR

The rate implied by the cash actually exchanged, so it carries fees. See the next section.

Cost per $1,000 borrowed

Total cost scaled to a unit, so loans of different sizes can be compared directly.

Interest-to-principal ratio

Cents of interest per dollar financed. Above 1.00 means you repay more in interest than you borrowed.

First-payment interest share

How much of instalment one is interest rather than repayment. The clearest measure of how front-loaded a loan is.

Halfway balance

What is still owed at the midpoint of the term — on long loans, far more than half.

Interest rate vs APR

The interest rate is the contractual rate on the note. It is what accrues on the balance and what the payment is built from.

The Estimated APR shown on this page is worked backwards out of the cash flows you entered: the money that actually reaches you at closing, against every instalment you actually pay. Because fees change that cash without changing the note rate, any fee pushes the APR above the rate. With no fees, the two match.

It is an estimate from your figures, not a lender's disclosure. A lender's legally disclosed APR follows its own regulatory rules about which charges are included, how odd days and rounding are treated, and which fees count as finance charges. Those rules differ by product and country. Use the figure here to compare offers you have entered on the same basis — not as a substitute for the APR on a loan agreement.

How loan term changes your real cost

A longer term buys a smaller payment with more interest, and the exchange rate is not intuitive. The calculator states it directly: the marginal cost of one extra year under the results shows exactly how much the payment falls and how much interest that costs, for your loan.

Two things follow. First, the saving per month shrinks as the term lengthens while the interest added keeps growing — the last year of term is the worst value. Second, a longer term raises the interest-to-principal ratio faster than it lowers the payment, which is why a long loan can cost more in interest than it ever advanced in principal.

How much does a lower interest rate save?

The rate sensitivity table under the results answers this for your figures, at two percentage points either side of the rate you entered. It reports both the payment change and the total-interest change, because a rate cut that looks small monthly can be large over a term.

The effect is not linear: the same one-point cut is worth more on a larger balance and far more on a longer term. That is why the table recomputes rather than scaling a rule of thumb. A rung that would fall below 0% is held at 0% and labelled, since a negative rate is not a loan this calculator models.

Do extra payments actually save money?

Yes, and the mechanism is worth understanding. An extra payment goes entirely to principal after that period's interest has been charged, so it reduces the balance that accrues interest for every remaining period. The saving compounds; it is not simply the extra amount times the rate.

The Extra payments mode models recurring, annual, one-time and dated payments together, reports the new payoff date against the original, and can solve the smallest extra payment that reaches a goal — a date, a number of months, or an amount of interest saved. It also models a prepayment penalty and reports the net saving after it, because some agreements charge for repaying early.

How much can I afford to borrow?

The Affordability mode works three ways: from a payment you already know you can make, from income and existing debt payments against a percentage cap you choose, or in reverse — what income would make a given payment a given share of it.

This is a budgeting estimate, not a lender qualification or approval decision. The percentage is deliberately yours to set: there is no universal limit, and lenders apply their own, which differ by product and by country.

Compare loan offers using total cost, not just monthly payment

The lowest payment and the cheapest loan are usually different loans. A longer term or a rolled-in fee lowers the instalment while raising everything you eventually pay.

The Compare loans mode puts up to three offers side by side on payment, rate, Estimated APR, fees, total interest, total borrowing cost, payoff date and cost per $1,000 — and reports the lowest payment, the lowest total cost and the lowest APR as three separate results. It does not name a winner, because which of those matters depends on whether your constraint is monthly cash flow or lifetime cost.

What is an amortization schedule?

An amortization schedule is the loan payment by payment: what each instalment is, how it splits between interest and principal, and what is left owing afterwards. Early payments are mostly interest because interest is charged on a large balance; as the balance falls, the same instalment repays more principal. That is why the split shifts even though the payment does not.

The schedule on this page carries the payment number, date, scheduled payment, principal, interest, any extra payment, cumulative interest and remaining balance, and exports to CSV with cumulative principal as well.

Common loan repayment structures

Fully amortizing (level payment)

One constant instalment repays interest and principal until the balance is zero. The default, and how most consumer loans work.

Equal principal

The same slice of principal every period, so the payment starts high and falls. Costs less interest overall than a level payment on the same term.

Interest-only with principal at maturity

Each instalment is exactly the interest; the whole balance falls due with the last payment.

Level payment with a balloon

The instalment amortizes down to a stated balance, which is then due in full at maturity.

Single payment at maturity

Nothing is paid until the end; interest capitalises into the balance.

All five are modelled here, and each closes at exactly zero with the principal column reconciling to the amount financed.

Loan types

This calculator is general: any fixed-rate instalment loan, in any currency, at any frequency. Where a loan type has its own rules, fees or repayment programmes, a dedicated calculator models them properly:

• Personal Loan Calculator — unsecured personal loans, with origination fees, Estimated APR and offer comparison.
• Mortgage Calculator — property loans, with taxes, insurance and PMI.
• Auto Loan Calculator — dealer worksheets, trade-ins, rebates and promo APR.
• Student Loan Calculator — federal repayment plans and forgiveness paths.
• Debt-to-Income Ratio Calculator — where a new payment leaves your ratio.
• Debt Snowball Calculator — ordering several debts for payoff.
• India EMI Calculator — EMI, processing fees and Indian lending conventions.

Methodology

The rate you enter is treated as a nominal annual rate compounded at the compounding frequency. Where the payment frequency differs from the compounding frequency, the two are reconciled through the effective annual rate — i = (1 + j/m)^m/p − 1, where j is the nominal annual rate, m compounds per year and p payments per year. When m and p match this collapses to j/m exactly, so an ordinary monthly loan keeps the textbook rate.

The Estimated APR is the internal rate of return of the borrower's cash flows — net cash at closing against every instalment, extra payment and penalty — annualised nominally, the Regulation Z convention. The effective (compounded) annualisation is reported alongside it.

Every figure on this page is produced in your browser by the same code the automated tests run. Nothing is uploaded, and no rate is fetched from anywhere: the calculator has no view on what rate you should be offered.

Calculation assumptions

Rounding

Full floating-point precision is carried through every calculation. Rounding to cents happens only at the display, copy and export boundary, so totals never drift from the schedule that produced them.

Final-payment adjustment

The last instalment is adjusted to bring the balance to exactly zero, absorbing the residue level-payment arithmetic leaves behind.

Fee treatments

A fee can be deducted from proceeds, added to the financed balance, or paid separately at closing. Contractual principal, financed balance, cash proceeds and upfront cash cost are kept separate throughout, and each treatment moves the Estimated APR differently.

Compounding and payment frequency

Independent. Semi-monthly and biweekly have no compounding counterpart, so they default to a monthly compounding basis and convert through the effective annual rate.

Extra payments

Applied to principal with the instalment of their period, after that period's interest and scheduled principal. They therefore reduce the balance that accrues interest in the next period. An extra larger than the balance is cut to exactly the balance.

Solvers

Loan amount and interest rate are found by bracketed bisection; the term by closed form; a payoff goal by bounded predicate bisection rounded up to the cent and re-verified. All are deterministic and bounded — the same inputs always give the same answer, and an impossible target returns a reason rather than spinning.

Limitations

Fixed rates only: variable and adjustable-rate loans are not modelled. Payment dates advance by whole periods and are not adjusted for weekends, holidays or day-count conventions. Interest accrues per period, not per day. Taxes, insurance and escrow are not included. Nothing here is a lender quotation, an eligibility test or advice.

Reference test cases

Each row is computed by the engine that runs this page, and each is separately pinned by an automated golden test. If the arithmetic ever changed, these figures would change and the test suite would fail before the page shipped.