See how an upfront finance fee changes APR while the contract interest rate still determines the scheduled payment. Enter the borrowed amount, annual interest rate, term, and fee withheld from the proceeds. The calculator solves for the monthly rate whose payment values equal the cash received, then annualizes that rate. It assumes equal monthly periods and no other charges. The CFPB defines APR as a yearly measure relating the value received to the amount and timing of payments. This model helps explain that relationship.
Worked formula check
The inputs come from CFPB installment-loan sample inputs. This check uses regular monthly periods, excludes the sample's odd first period and other charges, and calculates the outputs with the formula below. It is not a lender offer.
| Input or result | Value |
|---|---|
| Source balance | $5,000.00 |
| Source interest rate | 12% |
| Source term | 24 months |
| Modeled fee-free payment | $235.37 |
| Calculated fee-free APR | 12% |
| Calculated interest cost | $648.82 |
Enter the fee using the correct convention
The amount field is the balance used to calculate interest. The fee field is an upfront finance charge withheld from that amount when the loan is funded. Cash received is the amount minus the fee. The scheduled installment is still calculated on the full balance, so a fee changes the modeled APR without changing that installment. Enter only fees you have identified as finance charges for this comparison. The calculator does not decide whether a particular charge belongs in a lender's APR disclosure. It also does not model fees charged with every payment.
Understand the interest-rate result
The annual interest rate is converted to a monthly rate to calculate the fixed payment. That is the same payment formula used by the homepage and schedule generator. A fee-free calculation with equal monthly periods produces the same annual interest rate and modeled APR. Adding an upfront fee reduces the amount received but leaves the promised payments unchanged. The rate that discounts those payments back to the smaller amount must therefore be higher. You can see this relationship by changing only the fee and recalculating, while keeping the balance, interest rate, and term unchanged.
Understand the APR result
The model first finds the value of the scheduled monthly payments at a trial monthly rate. It adjusts that rate until the present value matches net proceeds. It then multiplies the monthly rate by the number of monthly periods in a year and expresses the result as a percentage. This is nominal annualization under the regular-period actuarial model, not an effective annual yield. The interest-plus-fee cost is a dollar amount rather than a rate, so it answers another useful question: how much the scheduled repayments exceed the cash received. Look at both results when checking a fee's effect.
Know when this model needs more detail
The first payment is assumed to fall one full month after funding. The tool does not accept an odd first period, irregular payment amounts, multiple advances, or a change in the interest rate. Those features need a more detailed cash-flow model. CFPB Appendix J contains the actuarial instructions for closed-end transactions, including transactions that have irregular timing. This page uses its regular single-advance relationship. A displayed modeled APR is not a substitute for the creditor's disclosure or a compliance calculation. If the disclosed APR differs, compare the amount financed, finance charges, payment dates, and payment schedule before drawing a conclusion.
How it works
Net proceeds = sum of A / (1 + i)^k, for k = 1 through n
Modeled APR (%) = i * 12 * 100
P is the loan balance, F is the withheld upfront finance fee, A is the regular monthly payment, and i is the solved monthly rate. The tool finds i by numerical iteration. The payment A uses the fixed-payment formula below.
r = annual interest rate (%) / 100 / 12
P is the interest-bearing balance, n is the number of monthly payments, r is the monthly rate, and A is the scheduled payment. At a zero interest rate, A = P / n. Each month, interest = opening balance * r; principal = payment - interest; closing balance = opening balance - principal.
This is the regular-payment form of the actuarial relationship in CFPB actuarial formulas, Appendix J. The schedule retains full precision internally and rounds amounts only for display. The model uses a fixed rate and equal monthly periods. It excludes daily accrual, irregular first periods, missed payments, and prepayment charges.
Frequently asked questions
What is the difference between APR and interest rate?
The interest rate represents the cost of borrowing before fees. The CFPB describes APR as a yearly measure relating value received to the amount and timing of payments. In this model a withheld finance fee changes APR.
How do I calculate APR from interest rate and fees?
Enter the loan amount, annual interest rate, term, and upfront finance fee. The tool solves for the rate that equates regular payments with the amount received after the fee.
Does APR equal interest rate with no fee?
Under this regular-monthly-period model, with no other charges, the modeled APR equals the entered annual interest rate.
Is the fee added to the borrowed balance?
No. This page models a fee withheld from the proceeds. The entered loan amount remains the interest-bearing balance, and cash received is that amount minus the fee.
Does this calculate APR for irregular payments?
No. The page assumes equal monthly installments beginning one month after funding. CFPB Appendix J describes actuarial calculations for more complex payment timing.