APR Calculator
Estimate a loan's annual percentage rate from its nominal rate, term and upfront fees.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
APR (%)
Dots show recalculated samples. Other inputs stay fixed.
About this calculator
This estimate solves for the annualized rate that makes the scheduled monthly payments equal the amount received after the upfront fee you enter. It assumes equal monthly payments and includes no charges beyond that fee. Official APR disclosures can include charges under rules specific to the loan and jurisdiction; use the lender's disclosure for an actual offer comparison.
Worked example
calculated with the default values below
Loan amount 20,000 $ · Nominal interest rate 6 % · Loan term 5 years · Upfront fees 500 $ APR 7.06 % · Monthly payment 386.66 $ · Total interest 3,199.36 $
Method and assumptions
PMT × (1 − (1+i)^−n) ÷ i = A − F; i ∈ [0, 1]; APR = 12i × 100 PMT uses r = note rate % ÷ 100 ÷ 12; i is found by bisection on [0,1] over 200 iterations; APR includes fees. This estimate solves for the annualized rate that makes the scheduled monthly payments equal the amount received after the upfront fee you enter. It assumes equal monthly payments and includes no charges beyond that fee. Official APR disclosures can include charges under rules specific to the loan and jurisdiction; use the lender's disclosure for an actual offer comparison. The references explain definitions and methods; any extra preset must be checked against the assumptions on this page.
Data sources
The references explain definitions and methods; any extra preset must be checked against the assumptions on this page.
Disclaimer
These calculators give estimates for general information only. They are not financial, tax or investment advice and do not take your personal circumstances into account. Before borrowing, investing or filing, confirm the numbers with a qualified adviser in your jurisdiction.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
PMT × (1 − (1+i)^−n) ÷ i = A − F; i ∈ [0, 1]; APR = 12i × 100
- i
- monthly rate solved for (decimal)
- PMT
- monthly payment at the note rate
- n
- number of payments
- A
- loan amount
- F
- fees
PMT uses r = note rate % ÷ 100 ÷ 12; i is found by bisection on [0,1] over 200 iterations; APR includes fees.
Frequently asked questions
Why is the APR higher than the interest rate I was quoted?
This estimator uses the nominal rate to calculate equal monthly payments, then solves for an annualized rate using the amount received after the upfront fee you enter. A lender's APR disclosure may account for other charges and timing under rules for that loan and jurisdiction. Treat this as a model estimate and compare it with the lender's official disclosure, not as a substitute for one.
What should I compare alongside APR when choosing a loan?
APR combines the entered interest rate and upfront fees into one annualised borrowing-cost estimate. Compare APRs for offers with comparable loan terms, then also check the monthly payment, total interest, upfront cash needed and any costs this calculator does not include. The lowest APR does not by itself tell you which payment schedule fits your budget.
Which inputs and limits apply to APR Calculator?
Use the units shown beside each field. These are form limits, not recommended settings. Loan amount: 1–100,000,000 $; Nominal interest rate: 0–100 %; Loan term: 1–50 years; Upfront fees: 0–100,000 $ PMT × (1 − (1+i)^−n) ÷ i = A − F; i ∈ [0, 1]; APR = 12i × 100 PMT uses r = note rate % ÷ 100 ÷ 12; i is found by bisection on [0,1] over 200 iterations; APR includes fees. This estimate solves for the annualized rate that makes the scheduled monthly payments equal the amount received after the upfront fee you enter. It assumes equal monthly payments and includes no charges beyond that fee. Official APR disclosures can include charges under rules specific to the loan and jurisdiction; use the lender's disclosure for an actual offer comparison. The references explain definitions and methods; any extra preset must be checked against the assumptions on this page.
What is a complete worked example for Loan amount = 20,000 $; Nominal interest rate = 6 %?
Inputs: Loan amount = 20,000 $; Nominal interest rate = 6 %; Loan term = 5 years; Upfront fees = 500 $. Calculation: PMT × (1 − (1+i)^−n) ÷ i = A − F; i ∈ [0, 1]; APR = 12i × 100. Results: APR = 7.06 %; Monthly payment = 386.66 $; Total interest = 3,199.36 $.