APR Calculator Calculate the Annual Percentage Rate including fees and charges for true loan cost comparison.

APR is the rate r that satisfies: Σ PMT/(1+r/12)^i = Loan Amount − Fees, for i = 1 to n months, where PMT is the monthly payment calculated at the stated interest rate. This is solved numerically using Newton's method: starting from the nominal rate as an initial guess, iteratively improving the estimate using f(r)/f'(r) where f(r) is the present value equation and f'(r) is its derivative. Convergence is typically achieved within 10-20 iterations. The APR exceeds the stated rate when fees are present because fees reduce the effective amount received while payments remain the same — you're paying interest on money you never actually received. For example, a $20,000 loan at 5% with $500 in fees means you only received $19,500 but make payments on $20,000, pushing the effective rate above 5%.