APR Calculator
Work out the annual percentage rate on a loan once origination fees and points are added to the interest rate.
What it does
The note rate is the rate the lender quotes. The annual percentage rate is the rate that tells you what the loan costs once fees are counted. United States lenders have to state the APR next to the note rate, and the gap between the two numbers is usually where the fees show up.
The method comes from Regulation Z, the truth in lending rules. The APR is the rate that equates the present value of all the required payments with the net amount of credit you actually receive. If a lender charges you a $200 origination fee on a $10,000 loan, you receive $9,800 and repay the loan as if you had borrowed $10,000, so the APR has to be higher than the note rate to make the numbers line up.
The calculation here follows the same path. It works out the monthly payment from the note rate, subtracts the prepaid finance charges from the loan to get the amount financed, then solves for the rate that discounts the same payments down to that smaller number. The answer is reported as a nominal annual rate, which is the monthly rate multiplied by twelve.
Not every charge belongs in the figure. Regulation Z treats prepaid finance charges such as origination fees and points as part of the amount financed, while late payment charges, penalties and charges for optional services are excluded. Some real estate closing costs can also be excluded under specific rules. This tool takes one line for the charges you want to include, so you decide what goes in.
APR is a comparison tool rather than a price. Two loans can carry the same APR and cost different amounts over the life of the loan if the payment schedules differ, and a lower APR on a longer term can cost more in total interest than a higher APR that is paid off sooner.
How to use
- Enter the loan amount the lender agreed to make.
- Enter the note rate, which is the interest rate before fees.
- Enter the term in years, with monthly payments.
- Add the origination fee or any other prepaid finance charge in dollars.
- Add discount points as a percentage of the loan amount if you paid any.
- Read the APR, then compare it with the note rate to see what the fees cost you.
Formula
- L
- Loan principal, the face value of the loan.
- j
- Monthly note rate, the annual rate divided by twelve.
- n
- Number of monthly payments.
- A
- Amount financed, which is the principal minus prepaid finance charges.
- i
- Monthly rate that discounts the payments back to the amount financed.
The tool assumes a fixed rate loan with equal monthly payments and the first payment one month after the advance. Regulation Z asks for the rate to be stated as a nominal annual rate, so the monthly rate is multiplied by twelve rather than compounded. Loans with irregular payments, deferred interest, or a first payment at closing need the full actuarial method from Appendix J of Regulation Z, which this page does not attempt.
Worked example
Example: $10,000 at 12% for one year with a $200 fee
Defaults: $10,000 loan, 12% note rate, 1 year term, $200 in prepaid finance charges, no points.
- Monthly rate: 12% / 12 = 1%.
- Payment: $10,000 x 0.01 / (1 - 1.01^-12) = $888.49.
- Prepaid finance charges: $200, so the amount financed is $10,000 - $200 = $9,800.00.
- Solve for the monthly rate that discounts $888.49 payments to $9,800: 1.3212% a month.
- APR = 1.3212% x 12 = 15.85%.
- Total interest is $861.85 and the fee costs $413.24 once you add the interest charged on the $200.
- The tool shows an APR of 15.85%, a payment of $888.49, $9,800.00 financed, $861.85 of interest and a fee cost of $413.24.
Reference table
| Prepaid charge | Amount financed | APR | Cost of the charge with interest |
|---|---|---|---|
| $0 | $10,000.00 | 12.00% | $0.00 |
| $100 | $9,900.00 | 13.91% | $206.62 |
| $200 | $9,800.00 | 15.85% | $413.24 |
| $400 | $9,600.00 | 19.83% | $826.47 |
| $800 | $9,200.00 | 28.14% | $1,652.95 |
Limits
- Assumes a fixed rate loan with equal monthly payments and no prepayments.
- Only the charges you enter are treated as prepaid finance charges, so the APR can differ from the one on a disclosure.
- Ignores taxes, insurance and any payment timing that differs from the monthly schedule.
- Does not produce the regulatory APR for loans with irregular payments, so treat those as an estimate.
Common mistakes
- Assuming the APR is the note rate plus the fee divided by the loan amount, which is not how the rate is defined.
- Leaving out points because they feel like part of the rate, when a point is a prepaid finance charge that reduces the amount financed.
- Adding late fees and penalties to the fee box, since Regulation Z excludes those charges.
- Comparing an APR on a 30 year loan with an APR on a 3 year loan as if they cost the same.
- Forgetting that the APR rises more slowly than the fee in percentage terms, so big fees look smaller in the rate than they are in dollars.
Try it yourself
Quick checks. Answers sit tucked under each question.
A $25,000 loan at 7% for 5 years comes with 2 points and a $400 fee. What is the APR?
Prepaid charges are 2% x $25,000 = $500 plus $400, so $900. The amount financed is $24,100 and the payment is $495.03. The APR works out at 8.55%.
What is the APR on a $10,000 loan at 12% for one year with no fees at all?
There are no prepaid charges, so the amount financed is the full $10,000 and the APR equals the note rate of 12.00%.
On the example loan, how much does the APR change if the fee doubles from $200 to $400?
The APR moves from 15.85% to 19.83%, a rise of 3.98 percentage points, and the dollar cost of the charge goes from $413.24 to $826.47.
Questions
What is the difference between the note rate and the APR?
The note rate is the interest rate on the amount you borrowed. The APR is the rate that also counts the prepaid finance charges, so it is the closer number to what the loan actually costs.
Why does a $200 fee push the APR up by nearly four points on a $10,000 loan?
The fee is two percent of the loan, so you receive $9,800 and repay it as a $10,000 loan over a year. A rate that equates the payments with $9,800 has to be well above 12%, and the gap widens as the term gets shorter.
Do all closing costs belong in the APR?
No. Regulation Z excludes late payment and similar penalties, and some real estate related charges such as title work and notary fees can be excluded under specific conditions. The rule you must follow is to include charges imposed by the creditor for the credit itself.
Is a lower APR always the better loan?
No. A lower APR on a longer term can cost more money overall than a higher APR that is repaid sooner, because more interest is paid in total. Compare the APR, the payment and the total cost together.
Does this tool handle car loans and mortgages?
Yes, both are fixed rate loans with monthly payments. Keep in mind that a mortgage has many other charges, and only some of them belong in the APR figure.
Why is the APR stated as a nominal rate?
Regulation Z asks for a nominal annual rate, which is the periodic rate multiplied by the number of periods in a year. It is not compounded, so the APR can read lower than the effective annual yield on the same loan.
Sources
- Consumer Financial Protection Bureau: 12 CFR 1026.22, annual percentage rate for closed end credit
- Electronic Code of Federal Regulations: 12 CFR 1026.22
- Office of the Comptroller of the Currency: Truth in Lending Act examination handbook