APR Calculator

Rate versus APR, concretely

In the worked example — a fictional $200,000 loan at a 6% note rate over 30 years with $4,000 of upfront fees — the payment is computed on the full $200,000: $1,199.10 a month, the standard amortized-loan (PMT) figure with monthly compounding. But the fees mean you effectively received only $196,000. The rate that reconciles 360 payments of $1,199.10 with that smaller amount is 6.19%: the fees added 0.19 percentage points to the cost of borrowing. Every number on this page was computed by the same tested engine when the page was built, on illustrative inputs chosen for the arithmetic, not quotes.

The example's loan, rate and term are the reference loan the methodology page validates the engine against. Recomputed here, the payment is $1,199.10 and the month-by-month schedule records $231,676 of interest and $431,676 of payments in total, matching the methodology page's figures. Note what the fees did not change: the payment and the interest total are identical with or without them. The fees enter the arithmetic in exactly one place — they shrink the amount the payments are measured against. The check is direct: feed $196,000 at 6.19% over 30 years back into the ordinary payment function and it returns $1,199.10, the same payment to the cent. With the fees field at $0 the net amount is the full $200,000 and the search settles on the note rate itself: 6%.

What the engine does with your four inputs

The form hands your four inputs to one engine function, which validates them, runs the steps below in order, and returns a typed result or an explicit, human-readable error. The interface formats what comes back; its fifth result line restates the returned APR as its distance above the rate you typed — the difference between two figures already on screen, described under "How to read the result" below.

1. Validation. The loan amount must be greater than zero, and the fees cannot be negative and must be less than the loan. The rate and term are checked by the payment function it calls next, like every other amortized loan on the site, and the term then becomes a whole number of monthly payments — years × 12, rounded to the nearest month: 360 here.
2. The payment at the note rate. The ordinary payment function runs on the full loan: $200,000 at 6% over 360 months gives $1,199.10. The fees do not touch this step; the Loan Calculator shows the same payment for the same loan, rate and term.
3. The net amount received. Loan minus fees: $200,000 − $4,000 = $196,000. The fees are not added to the payments or the interest total, and not spread over the term as a line of their own.
4. The search. The engine does not rearrange the payment formula for the rate; it searches by bisection on the monthly rate: the present value of the payments is strictly decreasing in the rate, so each trial rate is either too low or too high and the interval halves until it closes — the function header notes that convergence is guaranteed for this reason. The final monthly rate, multiplied by twelve and expressed as a percentage, is the APR.
5. The result. Three fields come back — the payment, the solved APR and the fee total echoed as entered: $1,199.10, 6.19% and $4,000 for the example. The companion guide derives each step on its own fictional loan.

Two fictional offers on one scale

A quoted rate and a fee total describe a loan in two numbers; the APR puts them on one scale. Consider two invented offers on the same $200,000 over 30 years: Offer A at a 6.25% note rate with $1,500 of upfront fees, Offer B at 6% with $8,000. Because its note rate is lower, Offer B's payment is lower — $1,199.10 against $1,231.43, $32.33 a month less, an ordering the build re-checks against the engine — and its fees are $6,500 higher.

Run through the engine, Offer A has the lower APR. The direction is set by how the fee difference, spread across 360 payments, weighs against the rate difference — the arithmetic, not the headline rate, settles it. The schedules behind the two payments record $243,316 of interest for Offer A and $231,676 for Offer B; the fees sit outside both totals and inside both APRs. The engine compares; which trade-off suits a particular household is not a question the arithmetic answers.

The same fee over a shorter term

The term is the other input that moves the gap. Keep the example's $200,000, 6% and $4,000 of fees but set the term to 15 years. The payment rises to $1,687.71 and the APR comes out at 6.32% — 0.32 percentage points above the note rate, against 0.19 over 30 years. The fee is 2% of the loan in both cases; what changed is the number of payments it is spread across, 180 instead of 360. A fixed amount divided among fewer payments weighs more on each, so a larger annual rate is needed to reconcile them.

Fees in dollars, points as a percentage

The fees field takes one dollar total — the label reads "Upfront fees & points (total)" — and the engine does not distinguish between kinds of charge. The engine prices points as a percentage of the loan, so they are converted first: one discount point costs 1% of the loan amount — the engine's own convention (its points function prices a point at 1% of the loan, as the methodology page states, and the build re-checks that identity), a definition rather than a market quote. The Mortgage Discount Points guide covers what points are. On the $200,000 example loan, 1.5 points is $3,000, as the points function prices it; entered alone, the APR is 6.14%. Add $1,000 of other upfront charges and the total is $4,000 — the worked example's fee total — and the APR is 6.19% again, because the engine sees only the sum. What points buy in return is the Mortgage Points Calculator's arithmetic, not this one's.

How to read the result

The result box shows five lines. Four are formatted from the engine's result and your inputs without further arithmetic; the fifth, "What the APR tells you", restates the returned APR as its distance above the rate you typed, in percentage points — the difference between two figures already on screen, 0.19 for the example:

• The large "% APR" figure is the solved rate, shown to at most two decimals. It is never below the note rate: equal when the fees are zero, higher as the fees rise or the term shortens.
• Note (quoted) rate is the rate you typed, echoed back beside the APR.
• Monthly payment is the ordinary amortized payment on the full loan at the note rate — $1,199.10 for the example. The fees field does not change it.
• Upfront fees is your fee total, echoed in whole dollars.
• What the APR tells you is the APR minus the note rate in percentage points — 0.19 for the example — stated as the amount the fees add to the cost of borrowing.

Internally every calculation keeps the full precision of IEEE-754 double-precision arithmetic, and nothing is rounded between steps; money is shown to the cent — or to whole dollars for large totals such as lifetime interest — and percentages to a small number of decimals. Your lender's figure may differ by a few cents depending on their rounding and day-count conventions — the difference is presentational, not an error.

Where the calculator stops

The limits are the engine's. It takes one number for fees and does not decide which charges belong in it. The fees are treated as paid upfront, subtracted from the amount received: a charge rolled into the balance belongs in the loan amount field, where it changes the payment, not in the fees field. The discounting uses every scheduled payment to the end of the term; a loan paid off earlier is a different calculation this function does not perform. The payment it starts from is the fixed-rate, fully amortizing payment, and the methodology page's limit applies in full: the calculators do not model adjustable-rate mortgages, interest-only periods, balloon payments, or negative amortization — the Fixed vs. Adjustable Rate guide describes the structure this engine does not price. And a correct calculation can still be the wrong calculation for your situation — choosing the right loan for a real-world decision is judgment we cannot automate.

Common misreadings

"A fee of 2% of the loan adds 2 percentage points to the APR." It does not. The $4,000 in the example is 2% of the loan and adds 0.19 points over 30 years, or 0.32 over 15. The fee is restated as a rate across every scheduled payment; over the 180 and 360 payments here its annual weight is a fraction of its share of the loan, and the fewer the payments, the closer to — or beyond — that share it climbs.

"The lower note rate has the lower APR." The note rate is one of two inputs that set the APR; the fee total is the other. In the two offers above the lower note rate belongs to Offer B and the lower APR to Offer A. The table is the check, not the headline rate.

Frequently asked questions

Not financial advice: a general educational estimate. Regulatory APR definitions specify exactly which fees count and can differ from a simple all-fees calculation — the lender's formal disclosure governs. Values are processed locally in your browser and never transmitted. See the methodology page.