Total finance charge (interest + fees): $235,676.38
What This Means
Fees push the true cost 0.189 percentage points above the 6% note rate — compare this APR, not the note rate, across lenders.
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Disclaimer
This calculator provides estimates for informational purposes only and does not constitute financial, medical, legal, or tax advice. Always consult a qualified professional about your specific situation.
How This Calculator Works
APR (Annual Percentage Rate) is a loan’s true yearly cost once upfront fees are folded in —
almost always higher than the interest rate printed on the loan quote. Enter the loan amount,
the lender’s stated interest rate, the term, and any fees or closing costs, and this calculator
finds the effective APR.
Lenders quote an interest rate, but that rate alone doesn’t capture the full cost of borrowing.
Origination fees, discount points, and other closing costs are typically subtracted from what
you actually receive — even though you keep making payments calculated on the full loan
amount. The APR expresses this gap as a single, higher rate, which is exactly why U.S. federal
law (the Truth in Lending Act) requires lenders to disclose it: it’s the one number that lets
you fairly compare two loan offers with different fee structures, not just their headline rates.
The Formula
There’s no simple closed-form formula for APR — it has to be solved numerically, but it leans on
the same fixed-rate amortization formula as the
Mortgage Calculator:
M=P×(1+r)n−1r(1+r)n
Compute the monthly payment M from the full loan amount, P, at the stated
interest rate (this is your real monthly bill — fees don’t change it).
Find the rate r that would produce that same payment M if P were
instead the amount actually financed (loan amount minus fees).
That rate, annualized, is the APR.
Since a higher discount rate always produces a lower present value for a fixed payment stream,
this calculator numerically searches for r using bisection — repeatedly narrowing a
range until it converges on the answer.
Worked Example
A $200,000 loan at a 6% stated interest rate, a 30-year term, and
$4,000 in fees:
Monthly payment (based on the full $200,000 at 6%): $1,199.10.
Solving for the rate r that produces a $1,199.10 payment on $196,000 over
360 months gives an effective monthly rate that annualizes to ≈ 6.19% APR —
noticeably higher than the 6% note rate.
Total finance charge (interest plus fees) over the life of the loan: ≈ $235,676.
Cómo funciona esta calculadora
La TAE (Tasa Porcentual Anual) es el costo anual real de un préstamo una vez que se incorporan
las comisiones iniciales — casi siempre más alta que la tasa de interés impresa en la cotización
del préstamo. Ingresa el monto del préstamo, la tasa de interés declarada por el prestamista, el
plazo y cualquier comisión o costo de cierre, y esta calculadora encuentra la TAE efectiva.
Los prestamistas cotizan una tasa de interés, pero esa tasa por sí sola no refleja el costo total
de pedir prestado. Las comisiones de originación, los puntos de descuento y otros costos de cierre
normalmente se restan de lo que realmente recibes — aunque sigues haciendo pagos calculados sobre
el monto completo del préstamo. La TAE expresa esta diferencia como una sola tasa, más alta, y
por eso la ley federal de EE. UU. (la Truth in Lending Act, o Ley de Veracidad en los Préstamos)
exige a los prestamistas divulgarla: es el único número que te permite comparar de forma justa dos
ofertas de préstamo con estructuras de comisiones distintas, no solo sus tasas anunciadas.
La fórmula
No existe una fórmula simple y cerrada para la TAE — hay que resolverla numéricamente, pero se
apoya en la misma fórmula de amortización a tasa fija que la
Calculadora de Hipoteca:
M=P×(1+r)n−1r(1+r)n
Calcula el pago mensual M a partir del monto total del préstamo, P, a la tasa
de interés declarada (esta es tu factura mensual real — las comisiones no la modifican).
Encuentra la tasa r que produciría ese mismo pago M si P fuera en
cambio el monto realmente financiado (monto del préstamo menos comisiones).
Esa tasa, anualizada, es la TAE.
Dado que una tasa de descuento más alta siempre produce un valor presente más bajo para una serie
de pagos fija, esta calculadora busca numéricamente r mediante bisección — reduciendo
repetidamente un rango hasta converger en la respuesta.
Ejemplo resuelto
Un préstamo de $200,000 con una tasa de interés declarada del 6%, un plazo de
30 an˜os y $4,000 en comisiones:
Pago mensual (basado en el monto total de $200,000 al 6%): $1,199.10.
Monto realmente financiado: $200,000−$4,000=$196,000.
Al resolver para la tasa r que produce un pago de $1,199.10 sobre $196,000 a lo largo
de 360 meses, se obtiene una tasa mensual efectiva que, anualizada, da ≈ 6.19% de
TAE — notablemente más alta que la tasa nominal del 6%.
Cargo financiero total (intereses más comisiones) durante la vida del préstamo: ≈ $235,676.
Because it's the rate on a smaller amount. Fees and closing costs are subtracted from the amount you actually receive, but your monthly payment is still calculated on the full loan amount at the stated rate — so the same payments, applied to a smaller amount actually financed, work out to a higher effective rate. The only case where APR equals the interest rate is when there are no fees at all.
Is APR always the best way to compare loans?
It's the standard, legally-required way in the U.S. to compare loans with similar terms and fee structures. It's less useful for comparing loans of very different lengths (fees get spread over fewer or more payments) or for loans you plan to pay off early, since APR assumes you'll keep the loan for its full term.
What counts as a fee in this calculation?
Any upfront cost that reduces what you actually receive but doesn't reduce what you owe — origination fees, discount points, underwriting fees, and similar closing costs. Ongoing costs like property taxes or insurance premiums (already broken out separately by the Mortgage Calculator) aren't part of a loan's APR calculation.
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