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APR Calculator

Find the real APR of a loan after fees, points, and PMI. Compare the true annual cost of a general loan or a US mortgage — not just the note rate.

Any installment loan. Loaned fees add to the balance; upfront fees come out of pocket and raise APR.

ExampleSample values — edit any field to see your result.

$
years
months
%
$

Added to the loan amount (financed). You do not pay these out of pocket at closing.

$

Paid out of pocket at closing, before funds are disbursed. These raise the real APR.

Results update as you type.

Real APR

6.563%

Estimated result

Amount Financed
$100,000.00
Upfront Out-of-Pocket Fees
$2,500.00
Payment per Period
$1,110.21
Pay back
Every Month
Total of Payments
$133,224.60
Total Interest
$33,224.60
All Payments and Fees
$135,724.60

Principal, interest & fees

Principal 74%, Interest 24%, Fees 2%
  • Principal74%
  • Interest24%
  • Fees2%

Amortization schedule

PeriodInterestPrincipalBalance
Year 1$5,795.24$7,527.22$92,472.78
Year 2$5,330.98$7,991.48$84,481.29
Year 3$4,838.08$8,484.38$75,996.91
Year 4$4,314.78$9,007.68$66,989.23
Year 5$3,759.21$9,563.25$57,425.98
Year 6$3,169.37$10,153.09$47,272.88
Year 7$2,543.14$10,779.32$36,493.57
Year 8$1,878.30$11,444.16$25,049.41
Year 9$1,172.45$12,150.01$12,899.40
Year 10$423.06$12,899.40$0.00
Real APR6.563%

Find the real APR of a loan — the annualized cost after fees, not just the interest rate. The general tab handles any installment loan with compounding and pay-back options; the mortgage tab is the US monthly case with points and PMI.

Formula

The contractual payment amortizes the amount financed at the note rate. For a periodic rate r over n payments:

payment = P × r / (1 − (1 + r)^(−n))

r comes from the compounding / pay-back maps (n = (years + months/12) × ppy; daily uses a 365.25-day year):

discrete:     r = (1 + i/m)^(m/ppy) − 1
continuous:   r = exp(i/ppy) − 1

Loaned fees are added to P. Totals are round(payment × n, 2). Real APR is the IRR of the (cent-rounded) payment series against cash to the borrower (loan − upfront fees, not amount financed minus fees), then:

APR = round(12 × ((1 + r_irr)^(ppy/12) − 1) × 100, 3)

Mortgage PMI, when down is under 20%, is an extra monthly cash flow until remaining LTV drops to 80% of the house value.

A lower note rate with high fees can have a higher APR than a slightly higher rate with small fees. Rank offers by real APR, not the interest rate on the flyer.

What typically goes into a US mortgage APR

Usually includedUsually excluded
Origination and underwriting feesAppraisal and survey fees
Discount / origination pointsTitle insurance
Mortgage-broker and processing feesPrepaid taxes and insurance in escrow
PMI (while required)Builder warranties

Examples

General: $100,000 · 6% · 10 years · $2,500 upfront

Monthly compounding and monthly payments produce a $1,110.21 payment. You repay $133,224.60 over 120 months ($33,224.60 interest). Adding the $2,500 closing fee, the real APR is 6.563%.

Mortgage: $350,000 house · 20% down · 6.2% · 30 years

The $280,000 loan pays $1,714.91 a month. $3,500 of fees plus 0.5 points raise the real APR to 6.367%. All payments and fees total $620,868.73.

Frequently asked questions

What is APR, and how is it different from the interest rate?
The interest rate is the cost of borrowing the principal only. APR (annual percentage rate) is the all-in annualized cost: it folds in origination fees, points, and other finance charges so you can compare lenders on equal footing. The Truth in Lending Act requires US lenders to disclose APR.
How is real APR calculated?
The calculator first finds the regular payment from the note rate and the amount financed. Upfront fees (and mortgage points) reduce what you actually receive. Real APR is the internal rate of return of that payment stream against those net proceeds, annualized by converting the periodic rate to a monthly equivalent and multiplying by 12. Loaned fees are added to the balance instead of reducing proceeds.
What is the difference between loaned fees and upfront fees?
Loaned fees are rolled into the loan — they increase the amount you repay but are not due at closing. Upfront fees are paid out of pocket before funds are disbursed, so you receive less than the face amount and the APR rises. Mortgage points work like upfront fees: one point is 1% of the loan.
When is PMI included in mortgage APR?
Private mortgage insurance is included only when the down payment is under 20%. It is charged each month until the remaining balance falls to 80% of the original house value, then it stops. PMI at 20% down or more is ignored, even if you enter a premium.
Why can APR understate the cost if I pay the loan off early?
APR spreads upfront fees over the full term. If you sell or refinance early, those fees are concentrated over fewer years, so the true cost is higher than the quoted APR. Between two loans with the same APR, the one with lower upfront fees is usually better if you expect to pay off early.

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