APR Calculator
Enter the loan amount, upfront fees, interest rate and term to see the monthly payment and the true APR once fees are counted. A built-in converter turns APR into APY and back for any compounding frequency.
Loan APR with fees
APR ↔ APY converter
–| Compounding | APY |
|---|
How to use the APR Calculator
- Enter the loan amount and the upfront fees, either as an amount or as a percentage of the loan.
- Tick the financed box if the fees are added to the balance instead of being paid or deducted upfront.
- Enter the nominal interest rate and the term in years or months.
- Press Calculate APR to see the payment, the effective APR, the APY and the total cost.
- Use the APR ↔ APY converter below to compare savings rates or loan rates quoted with different compounding.
How APR is calculated
- Monthly payment: M = P × i ÷ (1 − (1 + i)−n), with P the balance, i the nominal rate ÷ 12 and n the number of months.
- Cash received: the loan amount minus any fees paid upfront (or the full amount if fees are financed into P).
- Solve for the APR: find the monthly rate x where M × (1 − (1 + x)−n) ÷ x equals the cash received. APR = 12 × x. There is no closed-form answer, so the calculator uses bisection followed by Newton's method.
- APY = (1 + x)12 − 1.
Worked example
A 10,000 personal loan at 6% for 36 months with a 300 origination fee taken out of the proceeds:
- Monthly payment: 10,000 × 0.005 ÷ (1 − 1.005−36) = 304.22.
- You receive 9,700, so solve 304.22 × (1 − (1 + x)−36) ÷ x = 9,700, which gives x ≈ 0.6714% a month.
- APR = 12 × 0.6714% ≈ 8.06%; APY ≈ 8.36%.
- Total interest 951.90 + fees 300 = total cost of borrowing 1,251.90.
APR to APY reference
| APR | Annual | Quarterly | Monthly | Daily |
|---|---|---|---|---|
| 3% | 3.000% | 3.034% | 3.042% | 3.045% |
| 5% | 5.000% | 5.095% | 5.116% | 5.127% |
| 8% | 8.000% | 8.243% | 8.300% | 8.328% |
| 12% | 12.000% | 12.551% | 12.683% | 12.747% |
| 20% | 20.000% | 21.551% | 21.939% | 22.134% |
| 25% | 25.000% | 27.443% | 28.073% | 28.392% |
Frequently asked questions
What is APR?
APR (annual percentage rate) is the yearly cost of a loan including interest and most upfront fees, expressed as a percentage of the money you actually receive. Because it includes fees, it is usually higher than the nominal interest rate and is the better number for comparing loan offers.
How is APR with fees calculated?
First the monthly payment is worked out from the loan balance, nominal rate and term. Then the calculator finds the monthly rate at which those payments are worth exactly the cash you receive after fees, and multiplies it by 12. For 10,000 at 6% over 36 months with 300 in fees, the payment is 304.22 and the APR is about 8.06%.
What is the difference between APR and APY?
APR is a simple annual rate that does not include compounding within the year. APY (annual percentage yield) includes compounding, so it shows what you really earn or pay over a year. 12% APR compounded monthly is an APY of 12.68%.
How do I convert APR to APY?
Use APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. For continuous compounding APY = e^APR − 1. To go back, APR = n × ((1 + APY)^(1/n) − 1).
Does it matter if fees are financed?
Yes. If fees are paid upfront or deducted, you borrow the full amount but receive less cash. If they are financed, you receive the full amount but your balance and payments are higher. Both raise the APR, by slightly different amounts.
Why is a short loan's APR raised more by fees?
Fees are spread over the life of the loan. On a 2-year loan the same fee is recovered over fewer payments, so it adds more to the yearly cost than on a 30-year mortgage.
Is this the same APR a lender must disclose?
It follows the same actuarial method used for US Truth in Lending disclosures for a fixed-rate loan with equal monthly payments. Official disclosures may treat specific fees differently, so use your lender's figures for the final decision.