APR Calculator
Calculate the annual percentage rate including fees for any loan.
About the APR Calculator
This APR (Annual Percentage Rate) calculator reveals the true cost of a loan by converting the nominal interest rate plus upfront fees into a single annualized rate that reflects what you actually pay. Enter the loan amount, the nominal interest rate quoted by the lender, the upfront fees (origination, application, broker), and the loan term, and the tool returns the true APR — the number to use when comparing offers across lenders.
The distinction matters because two lenders quoting the same 7% nominal rate can have very different APRs depending on fees. A $10,000 loan at 7% with $200 in fees has a true APR of 7.609% — more than half a percentage point higher. A lender offering a slightly higher 7.25% rate with zero fees might actually be cheaper than the 7% loan with fees. APR is the great leveler.
The Truth in Lending Act (TILA) in the United States requires lenders to disclose APR alongside the nominal rate, but the disclosed figure sometimes excludes certain fees (PMI on mortgages, for example). Calculating APR yourself with this tool gives you a fully comparable figure.
How It Works
The calculator uses the Newton-Raphson method to solve for the rate i (monthly APR) in the loan amortization equation:
A = (PMT * (1 - (1 + i)^(-n))) / iWhere A is the loan amount, n is the number of monthly payments, and PMT is the monthly payment. The trick is that PMT is calculated on the net loan amount (principal minus fees), while the borrower receives the gross loan amount but repays based on the net.
Step 1: Compute the monthly payment on the net amount P = A - F using the nominal rate: PMT = (P * r) / (1 - (1+r)^(-n))
Step 2: Solve for the rate i that makes the same payment amortize the gross amount A over n months. This requires numerical methods because the equation cannot be solved algebraically for i.
The Newton-Raphson iteration starts with the nominal rate as the initial guess and refines it using the derivative of the payment function. The iteration typically converges in 5-15 steps to within 0.0001% precision.
Worked Examples
Suppose you borrow $10,000 at 7% nominal rate for 5 years, with $200 in upfront fees.
- Net loan received: $10,000 - $200 = $9,800
- Monthly payment on $9,800 at 7%/12: $9,800 * 0.005833 / (1 - 1.005833^(-60)) = $194.05/month
- Solve for the rate that amortizes $10,000 over 60 months at $194.05/month: APR = 7.609%
- APR premium over nominal rate: 7.609% - 7% = 0.609%
Now compare with a competing offer of 7.25% nominal rate with zero fees. Computing the APR gives 7.250% — lower than the 7.609% APR of the first offer, despite the higher nominal rate. The second lender is actually cheaper.
If fees were $500 instead of $200, the APR jumps to 8.486% — a full 1.5 points above the nominal rate. This is why comparing nominal rates alone is misleading.
When to Use This Tool
Use this APR calculator when:
- Comparing two personal loan offers with different rate/fee combinations
- Evaluating whether to pay discount points on a mortgage (pay upfront fee for lower rate)
- Deciding between a credit card with an annual fee and one without
- Assessing the true cost of a 'no-fee' loan that hides the cost in a higher rate
- Verifying the APR your lender disclosed on the Loan Estimate or truth-in-lending statement
- Comparing payday loans, title loans, and other high-cost credit products
- Calculating the effective APR on a 0% promotional offer with deferred fees
Lenders are required by law to disclose APR under the Truth in Lending Act. If your calculated APR differs significantly from the disclosed figure, ask the lender to explain which fees are and are not included.
Limitations & Disclaimer
This calculator computes APR using the Newton-Raphson numerical method on the standard amortization formula. It assumes a fixed-rate loan with level monthly payments for the entire term. It does not model variable-rate loans (where APR can change after origination), balloon payments, irregular payment schedules, credit-card-style revolving balances, or mortgage-specific fees like PMI and HOA. The APR figure is sensitive to the fee inputs — small errors in fees translate directly into small errors in APR. Always cross-check against the lender's official Loan Estimate or TILA disclosure. This is an educational tool, not a binding quote. See our disclaimer for full terms.
Frequently Asked Questions
What is the difference between APR and interest rate?
The interest rate (nominal rate) is the cost of borrowing the principal, expressed annually. APR includes the interest rate plus certain upfront fees (origination, application, broker, discount points), expressed as an annualized rate. APR is the more honest measure of true borrowing cost and is the better number for comparing loan offers.
What fees should I include in the upfront fees field?
Include origination fees, application fees, broker fees, discount points on a mortgage, and any other fees paid at closing that are financing costs. Do not include fees that are not financing-related, such as property taxes, homeowners insurance, or title insurance (which protect the lender but are not financing costs). For mortgages, your Loan Estimate will itemize which fees count toward APR.
Why is my calculated APR different from the lender's disclosed APR?
Possible reasons: (1) the lender may exclude certain fees from APR (e.g., PMI on conventional mortgages is sometimes excluded), (2) the lender may use a different day-count convention, (3) rounding differences, or (4) for credit cards, the issuer may use a different compounding assumption. If the difference is more than 0.1%, ask for clarification.
Does APR account for the time value of fees?
Yes — that is the entire point of APR. A $500 fee paid upfront costs more than a $500 fee paid at the end of the loan, because the upfront fee could have been earning interest elsewhere. APR captures this by computing the rate that makes the present value of all payments equal the net loan amount.
What is the difference between APR and APY?
APR is the annualized cost of borrowing, typically without intra-year compounding of interest. APY (annual percentage yield) is the annualized return on a savings account or investment, including intra-year compounding. The two are not directly comparable: a 7% APR loan and a 7% APY savings account are not equivalent rates.
How does APR work on credit cards?
Credit card APRs are typically quoted as nominal rates (e.g., 19.99% APR), and interest compounds daily. The effective APR on a credit card balance that is carried month-to-month is slightly higher than the nominal APR due to daily compounding. Paying the balance in full each month avoids all interest — the APR only matters if you carry a balance.
Last updated: July 21, 2026 · Author: HT99 Tools Editorial Team · Reviewed by: HT99 Tools Editorial Team