How it works
APR is the interest rate that makes the amount you actually receive equal to the present value of all your payments.
- Find the monthly payment at the stated rate: M = L × r(1 + r)n / ((1 + r)n − 1). If fees are deducted or paid at closing, L is the loan amount. If they are financed, L is the loan amount plus fees.
- Find the amount you actually receive, net of fees: loan amount − fees, or the full loan amount if the fees were financed.
- Solve for the monthly rate i such that net amount = M × (1 − (1 + i)−n) ÷ i.
- APR = i × 12. This matches the U.S. actuarial method for regular monthly payments.
There is no closed-form solution for i, so the calculator finds it numerically by bisection, to well beyond three decimal places. The finance charge is total payments minus the amount received: all interest plus fees.
Worked examples
$10,000 personal loan at 10% for 3 years with a $500 origination fee deducted
Monthly payment: $322.67. You receive $9,500.00. The rate that makes 36 payments of $322.67 worth $9,500.00 today is an APR of 13.562%, versus the 10% stated rate. Finance charge: $2,116.19. If the fee is added to the loan instead, the payment rises to $338.81 and the APR is 13.387%.
$300,000 mortgage at 6.5% for 30 years with $6,000 of points and fees
Payment: $1,896.20. Net amount received: $294,000.00. APR: 6.695%. Finance charge over 30 years: $388,633.47.
APR vs. interest rate
The interest rate determines your monthly payment. The APR adds the cost of upfront finance charges, spread over the loan term, to show the total yearly cost of borrowing. Under the federal Truth in Lending Act, lenders must disclose the APR so borrowers can compare loans with different rate and fee combinations. A loan with a lower rate but high fees can cost more than one with a slightly higher rate and no fees.
Why the term matters
Fees have a bigger effect on APR when the loan is short, because the cost is spread over fewer payments. The same $500.00 fee on a $10,000.00 loan at 10% produces an APR of 19.81% over 1 year but 13.56% over 3 years. On a 30-year mortgage, $6,000.00 of fees on a $300,000.00 loan adds only about 0.20 points to the rate.
The catch for mortgages: you may not keep the loan for its full term
Mortgage APR assumes you keep the loan for its full term. Most people sell or refinance much sooner, so upfront costs are spread over fewer years than the APR assumes. If you expect to move or refinance within a few years, a no-points, lower-fee loan can be cheaper even if its APR is a bit higher. The refinance calculator shows break-even timing.
What counts as a finance charge?
- Usually included: origination and underwriting fees, discount points, mortgage broker fees, prepaid interest, and mortgage insurance premiums.
- Usually excluded from mortgage APR: appraisal and credit report fees, title insurance, recording fees and other charges you would pay in a cash deal.
Rules are detailed and differ by loan type, so the APR on your Loan Estimate may differ slightly from this calculator. Enter only fees that are finance charges for the closest match.
APR vs. APY
APR is a simple annual rate: the monthly rate × 12. APY (annual percentage yield) includes compounding within the year and is used mainly for savings and CDs. A 12% APR with monthly compounding equals about a 12.68% effective annual rate. For savings comparisons, see the CD calculator.
Credit card APR
Credit cards have no upfront fee to spread, so the card's APR is simply its periodic rate times the number of periods in a year. Cards can have several APRs: purchase, balance transfer, cash advance and penalty. Balance-transfer fees are not included in the card's quoted APR, but you can estimate their effect here by entering the transferred balance, card rate, payoff period and fee.
How to use APR when shopping for a loan
- Get quotes on the same day for the same amount and term, because rates change daily.
- Compare APRs to see which offer is cheapest over the full term, then compare the upfront fees in dollars.
- Think about how long you will keep the loan. If you will likely pay it off early, favor lower fees. Rerun this calculator with a shorter term to see the effective cost over the years you expect to hold it.
- Read the Loan Estimate or TILA disclosure. It lists the APR, finance charge and amount financed. You can check those figures against this calculator.
Be wary of offers that advertise a low rate but bury the cost in fees, and of “no-fee” offers that make up for it with a higher rate. APR puts both on the same scale.
Points: paying fees to lower your rate
On mortgages, one discount point costs 1% of the loan amount and typically lowers the rate by a fraction of a percentage point. Points raise the APR above the rate, but they can still pay off if you keep the loan long enough. Divide the cost of the points by the monthly payment savings to find your break-even month, and buy points only if you expect to keep the loan well beyond it.
Frequently asked questions
What is APR?
The annual percentage rate is the yearly cost of a loan including interest and certain fees, expressed as a percentage. It lets you compare loans with different rates and fee structures.
Why is APR higher than the interest rate?
Because it includes upfront finance charges such as origination fees and points. You effectively receive less money but repay based on the full amount, which raises the true rate.
How do you calculate APR with fees?
Find the payment at the stated rate, subtract fees from the amount borrowed to get the net amount received, then solve for the interest rate that makes the present value of the payments equal to that net amount. This calculator does that automatically.
Is a lower APR always better?
Usually, if you keep the loan for its full term. If you will pay off or refinance early, upfront fees cost more per year than the APR implies, so a low-fee loan may be cheaper even with a higher APR.
What is the difference between APR and APY?
APR is a nominal annual rate (the periodic rate times periods per year). APY includes the effect of compounding within the year. APY is used for deposits, APR for loans.
Does APR include closing costs on a mortgage?
It includes finance charges such as points, origination and broker fees, and mortgage insurance, but excludes some third-party costs like appraisal, title insurance and recording fees.
If the interest rate is 0%, can the APR be higher?
Yes. A 0% loan with a fee has a positive APR, because you receive less than you repay.