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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.

$
%
The advertised or quoted rate (not APR)
years
$
Typical: 1-8% of loan amount
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Application, document, processing fees
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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:

Net Proceeds = Payment × [(1 − (1 + r)−n) / r]

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

Loan amount$28,000
Stated rate5.90%
Origination fee$420 (1.5%)
True APR6.21%
Monthly payment$541
Total cost$32,872

Offer B: Dealership — 6.5% + $0 fees

Loan amount$28,000
Stated rate6.50%
Origination fee$0
True APR6.50%
Monthly payment$548
Total cost$32,892

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

Mortgage amount$400,000
Rate without points6.125%
1 point cost$4,000
Rate with 1 point5.875%
Monthly savings$59/mo
Break-even68 months (5.7 years)

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.

FAQ

APR (Annual Percentage Rate) is the true annual cost of a loan including interest plus fees like origination fees, points, and other prepaid finance charges. The interest rate is just the cost of borrowing the principal. APR is always equal to or higher than the stated rate. Under TILA Regulation Z, lenders must disclose APR so borrowers can compare loans on equal terms.
APR is calculated using the Newton-Raphson iterative method as specified by TILA Regulation Z (12 CFR 1026.22). The algorithm finds the periodic interest rate at which the present value of all scheduled payments equals the net loan proceeds (loan amount minus prepaid finance charges). This rate is then multiplied by the number of periods per year to get the APR. The method converges to a precision of 1/8 of 1 percentage point as required by federal law.
APR (Annual Percentage Rate) is used for loans and does not account for compounding — it represents the cost of borrowing. APY (Annual Percentage Yield) is used for savings and investments and includes compounding: APY = (1 + r/n)^n - 1, where r is the nominal rate and n is the number of compounding periods. A 5% APR with monthly compounding equals approximately 5.12% APY. When borrowing, compare APRs. When saving or investing, compare APYs.
One mortgage discount point costs 1% of the loan amount and typically reduces your interest rate by 0.125% to 0.25%, depending on the lender. For a $400,000 mortgage, one point costs $4,000. Whether points are worth buying depends on the break-even period: divide the cost by the monthly savings. If you plan to stay past the break-even point (typically 5-7 years), buying points saves money. Points are also tax-deductible as prepaid mortgage interest in the year you purchase a home.
Your APR exceeds the quoted rate because it includes prepaid finance charges: origination fees (1-8% for personal loans, 0.5-1% for mortgages), discount points, mortgage insurance premiums, and other closing costs. The gap is larger when fees are high relative to the loan amount and when the loan term is shorter. For example, a 3% origination fee on a 1-year loan adds nearly 3% to the APR, but only about 0.6% on a 5-year loan because the fee is spread over more payments.

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