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APR Calculator

An APR calculator that folds up-front fees back into the rate. Borrow 25,000 at 7.5% over 60 months with a 500 origination fee and the true annual cost is 8.36%, on a payment of 500.95.

APR

8.36%

0.86 above the 7.50% quoted — the 500 fee, folded back into the rate.

Monthly payment500.95
Total cost30,056.92
Nominal rate7.50%what the lender quotes, before the fee

What the term does to the rate

the same loan and the same 500 fee, over every term

%
months

The fee is

The three terms the sixth question answers

Over 24 months9.51%2.01 points above the quoted rate
Over 60 months8.36%0.86 above — the term on the form
Over 120 months7.96%0.46 above; the fee is fixed and the term is not

How to use

  1. Enter the Loan amount from the offer, the Nominal interest rate the lender quotes, and the Term in months. A five-year loan is 60 there, not 5.
  2. Add up every compulsory up-front charge and put the total in Up-front fees. Origination, processing, administration, discount points. Anything you are free to decline stays out.
  3. Say how the fee is paid. Taken off the top means you receive the loan minus the fee; Added to the loan means you receive the full amount and repay the fee with it. The APR and the cards change as you type, so check Monthly payment against the lender's figure before you trust the rest.
  4. Do the same for the competing offer and compare the two APRs. Keep both URLs open in tabs if you want to flick between them.

Behind the scenes

Two lenders quote you 7.5% and only one of them is charging 7.5%. The gap is the fee you pay to get the money out of the door, and putting that fee back into the rate is the entire job of an APR calculator. That is also why regulators in most countries make lenders publish an APR alongside the headline number. The page opens on a worked case: 25,000 borrowed at 7.5% over 60 months, with 500 in up-front fees.

Two things happen as you type. The monthly payment comes out first, from the ordinary amortization formula applied to the full 25,000, because that is the amount the repayment schedule is built on. It works out to 500.95. Then the question turns around. You only ever received 24,500 once the fee came off the top, so what rate would make 24,500 generate a payment of 500.95 across 60 months? A bisection search halves the gap a hundred times and settles on 0.6963% monthly. Multiply by twelve and you get the 8.36% at the top of the page. The search widens its range until it holds the answer, so a short loan with a heavy fee gets its real figure: 300 of fees on 500 repaid a month later reads 1800.00%, not the edge of the search.

Total cost is simpler than it looks: the payment times the number of months, 30,056.92 on those defaults. If you want to check the whole thing hangs together, set Up-front fees to 0 and watch the APR drop onto exactly 7.50%. Under the cards, the same loan and fee are run over every term from 6 to 120 months, with your term marked, which is the quickest way to see how much of the APR is the fee and how much is the term. Every input rides in the page address, so the link you copy carries the exact comparison on your screen.

Good to know

  • The model is a fixed-rate, fully amortized loan. A teaser rate that steps up later or a variable APR will give you a number that is wrong rather than merely rough.
  • Fees taken off the top have to come to less than the principal or the calculation refuses to run, and past 100,000% a year it stops rather than guess. And the official APR your lender must disclose can differ from this one, because which charges count is set by regulation and varies by country. Use this to interrogate their figure. It is not financial advice.

Frequently asked questions

What's the difference between APR and the interest rate?

The interest rate prices the borrowing on its own. APR prices the borrowing plus the compulsory charges you had to pay to get it, expressed as one annual percentage. Where a loan carries fees, its APR always sits above its quoted rate.

Why is my APR higher than the rate I was quoted?

Fees. Your repayments are sized against the full principal, but the cash that reached you was the principal minus the fee. Paying full-size installments on a smaller amount received is a higher effective rate, and that is what the APR reports.

Which fees go in the box?

The charges you cannot avoid if you want the loan: origination or arrangement fees, processing and administration charges, discount points. Optional extras such as payment protection you were offered and could refuse usually stay out. If you are unsure, run it both ways and see how much the APR moves.

What if the loan has no fees at all?

Set Up-front fees to 0 and the APR lands on the nominal rate exactly, because the amount you received and the amount your repayments are sized against are then the same number. Any fee above zero pushes the two apart.

Does a shorter term push the APR up?

Yes, and by more than most people expect. The same 500 fee on the same 25,000 at 7.5% gives 8.36% over 60 months, 9.51% over 24 months, and 7.96% over 120. A fixed cost spread across fewer installments weighs much heavier on each one.

How is the APR actually worked out here?

Payment first, from the full principal at the quoted rate on the standard amortization formula. Then a bisection search for the monthly rate that reproduces that payment from the net amount you received. Annualize by twelve and you have the APR, which is a nominal APR in the American style rather than a compounded EAR.

How do I compare two loan offers with APR?

Put each offer in with its own principal, rate, term and fees, then line up the APRs and ignore the headline rates. The lower APR wins for that term. Glance at Total cost as well, because two offers at the same APR over different terms hand over very different sums in total.

The monthly payment doesn't match my lender's figure. Why?

Small differences usually come down to rounding, since a lender will round the installment up to the cent and may use a day-count convention rather than a flat twelfth of the annual rate. Bigger differences mean something is bundled in that you haven't entered here, typically insurance or escrow. If the fee was added to the balance, choose Added to the loan and the payment moves to match.

Can I send someone the numbers I'm looking at?

Copy the address bar. The loan amount, rate, term, fees and how the fee is paid are written into the URL as you edit them, so whoever opens the link sees the same inputs and the same answer. Useful for arguing about a mortgage offer with a partner who is on another laptop.

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