APR Calculator
Created by: Olivia Harper
Last updated:
Enter your loan amount, nominal interest rate, term, and upfront fees to calculate the true Annual Percentage Rate — and compare fee scenarios to see exactly how origination fees and points inflate your effective borrowing cost.
APR Calculator
FinanceEnter your loan details and upfront fees to calculate the true Annual Percentage Rate — and compare how different fee levels inflate your effective borrowing cost.
1 point = 1% of loan amount
Why APR Is the Right Number to Compare
When comparing loan offers, the interest rate only tells you what your monthly payment will be.
APR tells you the true cost of the loan by folding in origination fees, points, and other upfront charges into a single annual rate.
A loan advertised at 6.50% with $4,000 in fees may have a higher APR — and higher total cost — than a loan at 6.75% with no fees at all.
Under the Truth in Lending Act (TILA), U.S. lenders are required to disclose APR on all consumer loans.
This regulation exists precisely because the interest rate alone is insufficient for meaningful comparison when different lenders charge different fee structures.
APR is the standardized, legally required apples-to-apples metric.
How APR Is Calculated
APR is determined by finding the interest rate at which the present value of your scheduled loan payments exactly equals the net loan proceeds you actually receive — that is, the loan amount minus all upfront fees.
This requires numerical solving because there is no closed-form algebraic solution.
This calculator uses binary search (bisection method) across 100 iterations to find the monthly rate that satisfies the present value equation, then annualizes it by multiplying by 12.
The result is accurate to within a fraction of a basis point.
The fee sensitivity table then applies the same calculation across a range of fee levels so you can see exactly how each dollar of fee inflates your effective borrowing cost.
APR Calculation
Monthly payment = P × r(1+r)^n / ((1+r)^n − 1)
where P = loan amount, r = nominal monthly rate, n = term in months
APR: find rate R such that (P − fees) = Payment × (1 − (1+R)^−n) / R
Solve R using binary search (bisection) over 100 iterations
Annual APR = R × 12 × 100
Example Scenarios
$250,000 Mortgage — 6.50% Rate, $4,500 Fees
Loan: $250,000. Rate: 6.50% (30-year term). Monthly payment: $1,580. Fees: $1,500 origination + 1 point ($2,500) + $500 other = $4,500. Net proceeds: $245,500. True APR: 6.72%. The fees add 22 basis points above the stated rate. A competing lender charging 6.75% with zero fees has APR = 6.75% — more than the first lender's APR, making the first loan cheaper if held to maturity.
$20,000 Auto Loan — 7.99% Rate, $800 Fee
Loan: $20,000. Rate: 7.99% (60-month term). Monthly payment: $406. Origination fee: $800. Net proceeds: $19,200. True APR: 9.02% — over 100 basis points above the stated rate. On a short 5-year term, a flat fee has much larger APR impact than on a 30-year mortgage. This illustrates why comparing only the stated rate on short-term loans can be very misleading.
How People Use This Calculator
- Mortgage borrowers comparing offers from multiple lenders with different rate/fee combinations to identify the lowest true cost loan.
- Auto loan shoppers evaluating dealer financing with flat origination fees against bank or credit union offers with lower fees.
- Business owners analyzing SBA or commercial loan proposals where origination fees, guarantee fees, and points are common.
- Consumers refinancing existing loans who want to see how closing costs affect the true cost of the new loan versus keeping the old one.
- Anyone buying discount points and wanting to calculate how much the APR increases versus how much the monthly payment decreases.
Using APR for Smarter Loan Comparisons
APR is most reliable when comparing loans with the same term length and where you plan to hold the loan to maturity.
If you expect to pay off the loan early — or sell and refinance the property — compute total cash outflow (all payments + fees) over your expected holding period instead.
A high-fee, low-rate loan has a worse break-even for short-term holders even if its 30-year APR looks better.
When lenders quote APR, ask specifically which fees are included in their APR calculation.
Under TILA, certain fees must be included and others may be excluded depending on loan type.
Two lenders can quote the same APR while including different fee sets — one may be comparing APRs that include title fees while the other excludes them.
Always ask for the full fee schedule (the Loan Estimate for mortgages) and verify which items feed into the APR.
Frequently Asked Questions
What is APR and how does it differ from the interest rate?
The interest rate determines your monthly payment. APR includes the interest rate plus upfront costs — origination fees, points, and other lender charges — expressed as a single annual rate. APR is always equal to or higher than the stated interest rate and is the correct number to compare across loan offers.
How is APR calculated mathematically?
APR is the annual rate at which the present value of your scheduled payments equals the net amount you received (loan amount minus upfront fees). It is solved numerically — this calculator uses a binary search algorithm that converges in under 100 iterations to find the exact rate.
What counts as an upfront cost in the APR calculation?
Origination fees, discount points (1 point = 1% of loan amount), application fees, and certain closing costs paid to the lender. Third-party costs like appraisal, title insurance, and escrow may or may not be included depending on loan type and disclosure rules.
Is a lower APR always better?
Lower APR means lower total cost if you keep the loan to maturity. However, if you expect to pay off or refinance before the full term, a loan with higher APR but lower upfront fees may cost less in practice — because you pay fewer months of the higher rate before the loan is retired.
What are discount points?
Discount points are prepaid interest paid to the lender at closing in exchange for a lower interest rate. One point costs 1% of the loan amount and typically reduces the rate by 0.25%. Points raise your APR and make sense only if you hold the loan long enough to recoup the upfront cost through lower monthly payments.
Why does the APR on short-term loans seem very high?
Because upfront fees are amortized over the loan term. A $1,000 origination fee on a 24-month loan has a larger APR impact than on a 72-month loan because the cost is spread over fewer months. Short-term loans with flat fees can show very high APRs even with moderate stated rates.
Sources and References
- Consumer Financial Protection Bureau. "What is APR?" consumerfinance.gov, 2024.
- Code of Federal Regulations. "Truth in Lending (Regulation Z)." 12 CFR Part 1026, 2023.
- Fabozzi, F.J. "Fixed Income Mathematics." McGraw-Hill, 4th Edition, 2006.