APR Calculator
Calculate the true Annual Percentage Rate of any loan. See how fees inflate the real cost beyond the stated rate, compare offers side by side, and analyze whether mortgage points are worth buying.
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How to Use This Calculator
True APR tab
The default tab. Enter your loan amount, stated interest rate, and loan term. The calculator reveals the true APR after accounting for origination fees and other upfront charges. Expand "More options" to add additional fees or change the loan type. The result shows the gap between the stated rate and the true cost of borrowing.
Compare Offers tab
Enter two or three loan offers with different rate and fee combinations. The calculator computes the true APR for each offer and identifies which one is actually cheapest. A loan with a lower stated rate but higher fees can cost more than a "higher-rate" loan with no fees.
Points Analysis tab
For mortgages: enter your loan amount and rate, then specify how many discount points you want to buy. The calculator shows the break-even period — how many months until your monthly savings recoup the upfront cost of points. If you plan to stay in the home past the break-even point, buying points saves money.
Share your result
Every input is encoded in the URL. Click Share to send your exact scenario to a lender, partner, or financial advisor for comparison.
The Formula
APR is calculated using the Newton-Raphson iterative method, as required by TILA Regulation Z (12 CFR 1026.22). The algorithm finds the periodic rate r that satisfies:
Where:
Net Proceeds = Loan Amount − All Prepaid Finance Charges
Payment = Monthly payment based on the stated interest rate
n = Total number of monthly payments
r = Monthly periodic rate (APR = r × 12)
The solver iterates: rnew = rold − f(r) / f′(r)
until convergence within 0.0000001%
The key insight: you pay interest on the full loan amount, but you only receive the amount after fees. This discrepancy is why APR is always higher than the stated rate when fees are involved.
APR vs APY: APR does not account for compounding and is used for loans (cost of borrowing). APY = (1 + r/n)n − 1, includes compounding, and is used for savings (earning yield). A 5% APR with monthly compounding equals approximately 5.12% APY.
Example
David — comparing auto loan offers in Dallas, TX
David is financing a $28,000 used car over 5 years. He has two offers from different lenders and wants to know which one is actually cheaper.
Offer A: Credit union — 5.9% + 1.5% origination fee
Offer B: Dealership — 6.5% + $0 fees
Despite Offer A having a lower stated rate (5.9% vs 6.5%), its true APR (6.21%) is close to Offer B (6.50%). The total cost difference is only $20 over 5 years. In this case, the offers are nearly identical — David should consider other factors like prepayment flexibility and autopay discounts.
Points Analysis: David’s mortgage
David pays $4,000 upfront for 1 point, saving $59/month. He breaks even after 68 months. If he keeps the mortgage for the full 30 years, he saves $17,240 over the life of the loan.