# What is the APR of my loan?

Computes the annual percentage rate (APR) of a fixed-rate loan with monthly payments from the loan amount, interest rate, term and upfront fees, by the Regulation Z actuarial method.

- Page: https://www.acalculator.org/finance/apr-calculator
- JSON spec: https://www.acalculator.org/finance/apr-calculator.json
- Version: 687b6bbe993b

## Default answer

Example with the default inputs (Loan amount $25,000.00, Interest rate 6%, Loan term (months) 60, Upfront fees $750.00, Add the fees to the loan No): A $25,000.00 loan at 6% for 60 months with $750.00 of fees has an APR of 7.274% and a monthly payment of $483.32.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| amount | Loan amount | The amount you borrow, before any fees are taken off or added on. |
| rate | Interest rate | The yearly interest rate on the loan (the note rate), before fees. |
| term | Loan term (months) | The number of monthly payments. |
| fees | Upfront fees | Finance charges paid when the loan starts: origination fees, points, and other lender charges that count in the APR. |
| financed | Add the fees to the loan | On: the fees are borrowed on top of the loan amount. Off: you pay them at the start (or they are taken off the money you get). |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| apr | APR | The annual percentage rate: the yearly cost of the loan including the upfront fees. |
| payment | Monthly payment | The level monthly payment at the interest rate. |
| amountFinanced | Amount financed | The credit you actually get: the amount borrowed minus the upfront fees. |
| financeCharge | Finance charge | The dollar cost of the credit: all interest plus the upfront fees. |
| interest | Total interest | All the interest over the term: total of payments minus the amount borrowed. |
| total | Total of payments | The monthly payment times the number of payments. |

## Method

Payment = PMT(borrowed, rate ÷ 12, months). APR = 12 × j, where j is the monthly rate at which the payments’ present value, payment × (1 − (1 + j)^−n) ÷ j, equals the amount financed (loan amount minus upfront fees).

## Assumptions

- A fixed-rate loan with equal monthly payments, the first one month after the loan starts (no odd first period).
- Upfront fees are prepaid finance charges: they lower the amount financed whether you pay them in cash or add them to the loan.
- The APR is the Regulation Z actuarial APR: the monthly rate × 12, with no compounding into a yearly rate.
- Fees that are not finance charges (for example some title or appraisal fees on a mortgage) should be left out.

## Worked examples

1. amount = $20,000.00, rate = 5%, term = 60, fees = $500.00, financed = no gives apr = 6.047963%, payment = $377.42, amountFinanced = $19,500.00, financeCharge = $3,145.48, interest = $2,645.48. Source: Regulation Z appendix J actuarial method (APR = 12 × the monthly rate at which 60 payments of $377.42 are worth $19,500); hand calculation in content.mdx; Python bisection.
2. amount = $20,000.00, rate = 5%, term = 60, fees = $500.00, financed = yes gives apr = 6.02196%, payment = $386.86, amountFinanced = $20,000.00. Source: Regulation Z appendix J actuarial method with $20,500 borrowed and $20,000 financed; Python bisection.
3. amount = $25,000.00, rate = 6.5%, term = 72, fees = $0.00, financed = no gives apr = 6.5%, payment = $420.25. Source: Regulation Z: with no finance charge but interest, the APR equals the interest rate; hand calculation in content.mdx.
4. amount = $12,000.00, rate = 0%, term = 36, fees = $300.00, financed = no gives apr = 1.649977%, payment = $333.33, financeCharge = $300.00. Source: Regulation Z appendix J: a 0% loan with a $300 fee; 36 payments of $333.33 are worth $11,700 at 1.65% APR (Python bisection).

## FAQ

### What is the difference between the interest rate and the APR?

The interest rate is what the lender charges on the money you borrow. The APR is the yearly cost of the credit including upfront finance charges such as origination fees and points. With no fees the two are equal; fees push the APR above the interest rate.

### How is APR calculated?

First the monthly payment is worked out at the interest rate. The APR is then the yearly rate at which those payments exactly repay the amount financed: the loan amount minus the upfront fees. Regulation Z calls this the actuarial method; the monthly rate is multiplied by 12.

### What does $500 of fees do to a 5% car loan?

On $20,000 over 60 months at 5%, the payment is $377.42. You get $19,500 of credit after the fees, so the APR is the rate at which 60 payments of $377.42 repay $19,500: 6.05%.

### Which fees count in the APR?

Finance charges: fees you pay because you take the credit, such as origination fees, points, and many lender service charges. Fees you would pay in a cash deal, and some real estate fees such as title and appraisal fees, are not finance charges. Ask the lender for the Truth in Lending disclosure to see which fees they counted.

### Is it better to pay fees up front or add them to the loan?

Adding fees to the loan means you pay interest on them, so the finance charge is higher, but the APR is similar, because both count the fees as a cost of credit. $500 of fees on $20,000 at 5% for 60 months gives an APR of 6.05% paid up front and 6.02% added to the loan.

### How accurate does a lender's APR have to be?

For a regular loan, Regulation Z treats a disclosed APR as accurate if it is within 1/8 of a percentage point of the actuarial APR.

## Sources

- Regulation Z (Truth in Lending), 12 CFR 1026.22(a): APR by the actuarial method; accurate within 1/8 of 1 percentage point for a regular transaction. https://www.consumerfinance.gov/rules-policy/regulations/1026/22/
- Regulation Z, appendix J to part 1026: the actuarial method; the APR is the unit-period rate times the number of unit periods in a year. https://www.consumerfinance.gov/rules-policy/regulations/1026/j/
- Regulation Z, 12 CFR 1026.18(b): the amount financed. https://www.consumerfinance.gov/rules-policy/regulations/1026/18/
- Regulation Z, 12 CFR 1026.4: the finance charge; charges of a type payable in a comparable cash transaction are not finance charges, and 1026.4(c)(7) excludes real-estate fees such as title examination and appraisal fees. https://www.consumerfinance.gov/rules-policy/regulations/1026/4/
- Consumer Financial Protection Bureau, What is the difference between a loan interest rate and the APR? https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-loan-interest-rate-and-the-apr-en-733/