engineering fundamentals Advanced Annual Percentage Rate Calculator
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LoanIQ for iPhone is now available.
efunda's iPhone version of its online loan, lease, and APR calculators. Choose any variable (loan amount, payment, interest rate, etc.) as the unknown and calculate the result in real-time as other variables are entered. App Store
Advanced APR Calculator

Loan Amount (C)

*Extra Cost (E)

Interest Rate % (R)

Compound Frequency (m)

No. of Payments (N)

Payment Frequency (q)

APR (A): 
* The Extra Cost (E) is the lump sum of all extra costs involved in the loan, which include points, application fee, closing cost, processing fee, title fee, and so on. In short, it's the money you borrowed that you never saw.
This calculator first calculates the monthly payment using C+E as the total loan amount:
where r is the adjusted equivalent interest rate applied to the total loan amount C+E
The APR is essentially the actual interest rate applied to the intended loan amount C and can be calculated iteratively by solving the following equation using the Newton-Raphson method:
The annual percentage rate A is calculated using the following formula:
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