Turn a loan's rate and fees into its APR and effective annual rate, with a payment schedule. Runs on your device.
The APR is the yearly rate that makes the loan's payments, discounted at that rate, equal the money you actually received, so fees raise it above the stated interest rate. The page uses the actuarial method for equal monthly payments: it finds the monthly rate i where payment × (1 − (1 + i)^−n) ÷ i equals the money received, then APR = 12 × i. The US rule for this, Regulation Z Appendix J, defines the APR as the nominal rate found by multiplying the unit-period rate by the number of unit-periods in a year. A bisection search solves for i, so no table or guess is needed. The effective annual rate, (1 + i)^12 − 1, adds the effect of compounding twelve times a year.
The page opens on a 200,000 loan at 6% over 30 years with 4,000 of fees paid at closing. The payment is 1,199.10, worked from 200,000 at 6% and rounded to the cent, with a last payment of 1,200.16 to clear the leftover cents. You receive 196,000 after the fees, so the monthly rate that discounts 359 payments of 1,199.10 and that last payment of 1,200.16 down to 196,000 is 0.5158%, which makes the APR 6.189% and the effective annual rate 6.368%. With no fees the APR would equal the 6% rate. A small case you can check by hand: borrow 10,000 for one month at 12%, with a 100 fee at closing. You repay 10,100 and received 9,900, so i = 10,100 ÷ 9,900 − 1 = 2.0202% and the APR is 24.242%. Short loans with fees give high APRs.
If the fees are paid at closing, you borrow the full amount but receive less, so the payment is the same and the APR rises. If the fees are added to the loan, you still receive the loan amount, but you borrow and pay interest on loan plus fees. On the opening example, financing the 4,000 raises the payment to 1,223.08 and the total interest to 236,311.89, and the APR is 6.186%. The two APRs are close here because the financed fees pay the stated 6% rate on the extra 4,000. Which fees count depends on the transaction and the law (Regulation Z sets finance-charge rules, with exclusions for specific categories). The page counts only the fees you type, so enter the charges your lender or loan disclosure classes as finance charges and leave out the rest.
The page assumes a fixed rate, equal monthly payments and a first payment one month after the loan starts. It handles terms of 1 to 1,200 months and an APR up to 1,200%. It does not model variable rates, interest-only periods, balloon payments, a first period of odd length (the last payment is the only odd one), daily interest or the exact fee rules for a given country or product. A lender's disclosed APR follows its own legal rules and can differ from this estimate. Amounts are rounded to 2 decimals only when shown. Nothing you type is stored or sent. This is an estimate, not financial advice.
Find the monthly rate i where the payments, discounted at i, equal the money you received, then multiply by 12. For 200,000 at 6% over 30 years with 4,000 of fees paid at closing, i is 0.5158% and the APR is 6.189%. The page shows the equation with your numbers.
The interest rate sets the payment. The APR also counts the fees, so it shows the full yearly cost of the money you received. On the opening example the rate is 6.00% and the APR is 6.189%. Without fees the two are the same.
The APR is 12 times the monthly rate and does not include the effect of compounding. The effective annual rate does: (1 + i)^12 − 1. On the opening example the APR of 6.189% is an effective annual rate of 6.368%.
A fee is spread over few payments. Borrowing 10,000 for one month at 12% with a 100 fee costs 10,100 to repay against 9,900 received, which is 2.0202% in a month and an APR of 24.242%. The same fee on a 30-year loan adds only a small amount.
The page shows both so you can compare the APR, the payment and the total interest. On the opening example paying at closing gives 1,199.10 a month and 6.189%, and financing gives 1,223.08 a month and 6.186%. It does not tell you which to pick, because it cannot see your cash or other costs.
The numbers you type are processed in your browser and not uploaded. Nothing is saved when you close the page. The page counts visits with Google Analytics, and the amounts you type are not part of that.