Loan Calculator
Calculate the monthly payment, total interest and payoff cost for any fixed-rate loan, with the difference between rate and APR made explicit.
The two numbers on the screen do not multiply together
The monthly payment comes out of the formula with fractions of a cent in it — 2334.291426 on a 400,000 loan at 5.75% over thirty years. The screen shows 2,334.29, because money has two decimal places. So there are three defensible totals, and they are all different.
| How you get there | Total |
|---|---|
| Shown payment × 360 | 840,344.40 |
| Exact payment × 360 | 840,344.91 |
| What a lender actually collects — the figure shown above | 840,345.77 |
Anyone checking the arithmetic finds a discrepancy and reasonably wonders which figure is wrong. None of them is — they are answers to slightly different questions, and the question people usually mean is the third one, which is the one the calculator above now reports. Multiply its monthly figure by the term and you will not get its total; that is the honest outcome rather than a slip, and it says so.
A lender charges the rounded payment every month, and the balance does not land on exactly zero. Whatever is left is settled at the end, so the last payment is a different amount from all the others — 2,335.66 rather than 2,334.29 here. It can be larger or smaller, depending on which way the rounding went, and both happen among the loans below.
The gap has a ceiling, and it is half a cent per payment
Rounding to the nearest cent moves the payment by at most half a cent, so multiplying by the term cannot introduce more than half a cent times the number of payments. That is a hard bound rather than an estimate.
| Term | Most the totals can differ by |
|---|---|
| 36 payments | 0.18 |
| 60 payments | 0.30 |
| 120 payments | 0.60 |
| 360 payments | 1.80 |
A sweep of 1,000 combinations — principals from 10,000 to 500,000, five rates, four terms — found a worst case of 1.80 against a bound of 1.80. So the bound is not merely respected, it is very nearly reached, which is what tells you it is the right bound rather than a generous one.
There is exactly one case where the numbers on the screen do multiply out: when the payment happens to land on a whole number of cents. A 12,000 interest-free loan over 24 months is 500.00 a month, and every total agrees to the penny.
None of this changes a decision. It changes whether the figures can be checked, which is a different thing — and the honest summary is that a total-interest figure is good to about a dollar over thirty years, not to the cent it is printed with.
How to use
- Enter the amount, rate and term.
- Read the monthly payment and total interest.
- Compare a shorter term to see what it saves.
- Compare offers on APR, not on the headline rate.
Frequently asked questions
What is the difference between interest rate and APR?
The rate is the cost of borrowing alone; the APR includes fees and charges expressed as an annual rate. Two loans at the same rate can have very different APRs, which is precisely why APR exists and why it is the number to compare offers on.
Why does a longer term cost so much more?
Because you are borrowing the money for longer, so interest accrues over more years. Extending a term lowers the monthly payment and raises the total substantially — which is the trade being offered whenever a longer term is presented as making something affordable.
What does amortisation mean?
Paying a loan off through level payments that cover interest first and principal second, with the split shifting over time. Early payments are mostly interest because the balance is largest then, which is why a loan paid for two years may have barely reduced.
Do extra payments help much?
Substantially, and more the earlier they are made, because each extra pound of principal removes all its future interest. Check the lender applies overpayments to principal rather than to the next instalment — the two are not the same and the difference is the whole benefit.
What is a prepayment penalty?
A charge for paying off early, which exists because early repayment costs the lender expected interest. They are restricted in many places and not extinct, and the loan documents will say. It is worth checking before planning to overpay.
Can I rely on this figure?
As an estimate for comparing scenarios, yes. Actual offers depend on your credit, the lender's fees and the rate you are actually given, none of which this knows. Nothing here is financial advice, and a written offer is the only binding figure.
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