Effective Interest Rate Calculator — APR Including Fees
Enter the loan amount, nominal annual rate, term in months and any upfront origination fee to find the true effective interest rate (APR) — the annualised cost of the loan including the fee.
%
months
%
True annual cost of borrowing including fees — higher than the nominal rate
- 1
Monthly nominal rate
r = 8% ÷ 12 ÷ 100 = 0.006667The stated annual rate converted to a per-month decimal. - 2
Monthly payment (PMT)
20,000 × 0.006667 ÷ (1 − (1 + 0.006667)^−60) = 405.53 - 3
Net proceeds after fee
20,000 × (1 − 2% ÷ 100) = 19,600The borrower receives this smaller amount while still repaying the full PMT schedule. - 4
Effective annual rate (APR)
(1 + i_eff_monthly)^12 − 1 = 9.2282The effective monthly rate is found by solving net proceeds = PV(PMT, n); the result is then compounded to an annual rate.
How does this calculator work?
EIR (APR) = (1 + i_eff_monthly)^12 − 1, where i_eff_monthly is found by solving Net_Proceeds = PMT × (1−(1+i)^−n)/i. Net_Proceeds = loan minus the origination fee. The fee and compounding both push the effective rate above the nominal annual rate.
Formula
How this is calculated
A loan's nominal interest rate tells you only part of the story. Banks and lenders often charge upfront origination fees, arrangement fees or points that are deducted from the proceeds but not from the repayment schedule — you borrow 20,000 but receive 19,600 (after a 2% fee) while still repaying as if you borrowed 20,000. This makes the effective annual rate higher than the stated nominal rate.
The calculator computes the standard monthly payment using the nominal rate: PMT = P × i / (1 − (1+i)^−n), where i is the monthly rate and n is the number of months. It then finds the effective monthly rate i_eff that equates the net proceeds received (loan amount minus fee) to the present value of the payment stream: Net_Proceeds = PMT × (1 − (1+i_eff)^−n) / i_eff. This is solved numerically using bisection. The result is annualised as APR = (1+i_eff)^12 − 1.
This definition of APR is consistent with the EU Consumer Credit Directive and the US Truth in Lending Act approach of reflecting the true total cost of credit as an annualised rate. In practice, some fees (insurance, third-party fees) may or may not be included depending on jurisdiction; this calculator includes only the origination fee you enter. The loan balance chart shows the amortisation using the nominal rate.
Frequently asked questions
Two compounding effects push the EIR above the nominal rate. First, even without fees, monthly compounding of a nominal annual rate produces an EAR = (1 + r/12)^12 − 1 > r. Second, an origination fee reduces the net proceeds while keeping payments unchanged, so you are effectively paying more for less money — this further raises the true cost. A 2% origination fee on a 5-year loan can add roughly 0.7–0.8 percentage points to the effective annual rate.
In most regulatory frameworks, yes — APR (Annual Percentage Rate) is defined as the effective interest rate that discounts all cash flows (loan proceeds received, all payments made) to zero, then annualised. The EU and UK define it as the APRC (Annual Percentage Rate of Charge), annualised using continuous or monthly compounding. This calculator uses monthly compounding, which closely matches standard consumer-finance APR definitions.
A longer term spreads the origination fee over more payments, so the fee's impact on the effective rate is smaller for longer loans and larger for shorter ones. A $400 fee on a 12-month loan raises the effective rate significantly; the same fee on a 60-month loan has a much smaller effect. The nominal rate's compounding premium is independent of term.
Also known as
TG we-Calculate Editorial Team. (2026). Effective Interest Rate Calculator — APR Including Fees [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/effective-interest-rate-calculator
TG we-Calculate Editorial Team. "Effective Interest Rate Calculator — APR Including Fees." TG we-Calculate. 2026. https://we-calculate.com/calculator/effective-interest-rate-calculator.
TG we-Calculate Editorial Team, "Effective Interest Rate Calculator — APR Including Fees," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/effective-interest-rate-calculator
@misc{wecalculate_effective_interest_rate_calculator, title = {Effective Interest Rate Calculator — APR Including Fees}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/effective-interest-rate-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?