APR Calculator

How to Use the APR Calculator

A quoted interest rate describes the loan. The APR describes the deal. The gap between them is fees, and on small or short loans that gap can be enormous.

1. Enter the loan amount. The face value of the agreement — the figure the interest rate is applied to and the payments are calculated from.
2. Enter the fees. Arrangement fees, broker commission, documentation charges, mandatory insurance. Include anything you pay to get the loan, whether it is deducted from the advance or added to the balance.
3. Enter the quoted rate and term. The nominal rate the lender advertises, and how long the agreement runs.
4. Read the headline. That is the rate the loan actually costs once the fees are treated as part of the price of borrowing — which is exactly what consumer credit disclosure rules are designed to reveal.

The table at the bottom recalculates the APR at six different fee levels on the same loan, so you can see how quickly fees move the number. It is the fastest way to judge whether a fee is worth negotiating.

APR Formula

There is no closed-form solution for APR. It is defined implicitly — the discount rate at which the present value of every payment equals the amount you actually received — so it has to be solved numerically.

Note what the equation is really saying. The payments are fixed by the quoted rate on the full amount. The money in your hand is smaller. So the same payments are buying you less money, and the effective rate must therefore be higher.

Example

$20,000 at 6.9% over four years, with $600 of fees

1. Monthly rate: 0.069 ÷ 12 = 0.00575. Payments: 4 × 12 = 48.
2. Monthly payment on the full $20,000: $478.00.
3. Money you actually receive: 20,000 − 600 = $19,400.
4. Solve for the rate that discounts 48 payments of $478.00 back to $19,400: the monthly figure is 0.70670%.
5. Annualise it: 0.70670 × 12 = 8.480% APR against a quoted 6.9%.
6. Total repaid: 478.00 × 48 = $22,943.88. Total cost of credit: 22,943.88 − 19,400 = $3,543.88.

Why $600 became 1.58 percentage points

The fee is 3% of the loan. Spread across four years it does not add 0.75 points a year, because you never had the use of that money at all — you are paying interest on $20,000 while holding $19,400. Shorten the same loan to two years and the same $600 pushes the APR to roughly 10.2%, because there are half as many payments to spread it over.

That is the rule worth remembering: a fixed fee hurts more on a shorter loan. It is also why payday and short-term products post APRs in the hundreds — a modest fee compressed into a few weeks annualises brutally.

Why the Cheapest Headline Rate Is Often Not the Cheapest Loan

APR exists because comparing loans on their headline rate is unreliable. Two lenders can quote the same 6.9% and charge completely different amounts.

Read that table carefully. Lender C looks worse on the headline rate than Lender B and is cheaper in total. A one-point difference in quoted rate is worth less than a $600 fee on this loan, and no amount of staring at the advertised rates would have told you that.

Two cautions about APR itself. First, it assumes you keep the loan to term — repay a mortgage after five years and the fee is spread over five years rather than twenty-five, so the real APR you experienced is much higher than the one disclosed. Second, APR does not capture optional costs, penalties or the value of flexibility, all of which can matter more than a few tenths of a percentage point.

Four Practical Notes on APR

Four practical notes.

Fees deducted or added? Some lenders take the fee out of the advance, so you receive less; others add it to the balance, so you borrow more. This calculator models the first, which is the conservative reading. If your fee is being added to the loan, add it to the loan amount as well and set the fee field to zero — the resulting APR will be very close.

Representative APR is not your APR. Advertised rates in many markets need only be offered to a proportion of successful applicants — often 51%. The rate you are actually offered after a credit check can be materially higher, and it is the only one worth calculating with.

APR and APY are different animals. APY describes what a deposit earns and includes compounding. APR describes what a loan costs and includes fees. Comparing one against the other is comparing two different conventions.

Watch the term. Because APR annualises a fixed cost, extending a term lowers the APR while raising the total interest. A loan can look cheaper on APR and cost more in cash. Always check total cost of credit alongside the rate — the loan payment calculator shows the full repayment schedule behind it.

Early repayment changes everything. APR is calculated on the assumption that you run the loan to its final payment. Settle a four-year loan after eighteen months and the $600 fee has been spread over eighteen months rather than forty-eight, so the rate you actually paid is far above the disclosed 8.48%. If you expect to repay early, weight your comparison towards the loan with the lower fee rather than the lower rate — the fee is sunk on day one and the interest is not.

Compare like with like. Two APRs are only comparable when the terms match. A 7.2% APR over five years and a 7.9% APR over three are different products, and the cheaper-looking one costs more in cash. When the terms differ, the figure to put side by side is total cost of credit, which is the fourth tile on this page minus the third.

A final sanity check that takes ten seconds. Multiply the monthly payment by the number of payments, subtract what you actually received, and look at the result as a share of the money you got. On the worked example that is $3,543.88 against $19,400 — just over 18% of the advance, paid over four years. That single fraction is often more persuasive than any rate, because it is money rather than percentage points, and it is impossible to dress up with a favourable convention.