Loan APR calculator
Work out the APR of a loan including upfront and monthly fees, in both UK/EU and US conventions.
A clear answer. Here’s how.
The monthly payment on a level-payment loan is amount × i ÷ (1 − (1 + i)^−n) with i = rate ÷ 12. The APR is the rate that makes the present value of all payments equal what you actually receive (the amount less any upfront fee). The tool bisects on that rate: the monthly rate is the exact solution, the effective annual APR is (1 + monthly)^12 − 1 as in the UK and EU equation of equivalence, and the US nominal APR is the monthly rate × 12. With no fees the nominal APR equals the stated rate. Payments are assumed level, in arrears, one-twelfth of a year apart.
How this is checked
3 reference checks passed These 3 cases were run when this page was built, on 20 October 2026, and all reproduce within the stated tolerance. The same cases are part of the automated tests that run on every change to Toolmoz. Engine version 1.
See the checks and where each expected answer comes from
Case 1
- Inputs
- Loan amount 10000Interest rate (% a year, nominal) 6Term (months) 36Upfront fee, taken from the amount you receive 0Monthly account fee, added to every payment 0
- Expected, and what Toolmoz gave
- Monthly loan payment expected 304.2194, Toolmoz 304.2193745155571APR, nominal (monthly rate × 12, US convention) expected 6, Toolmoz 6.000000000001338APR, effective annual (UK and EU convention) expected 6.1678, Toolmoz 6.167781186451515
- Where the expected answer comes from
- 10000 × 0.005 ÷ (1 − 1.005^−36) = 304.2194 and (1.005)^12 − 1 = 6.1678%, in 50-digit decimal arithmetic
- Allowed difference
- ±0.001 absolute
Case 2
- Inputs
- Loan amount 10000Interest rate (% a year, nominal) 6Term (months) 36Upfront fee, taken from the amount you receive 200Monthly account fee, added to every payment 0
- Expected, and what Toolmoz gave
- Monthly loan payment expected 304.2194, Toolmoz 304.2193745155571Total cost of credit (interest and fees) expected 1151.8975, Toolmoz 1151.8974825600562APR, nominal (monthly rate × 12, US convention) expected 7.3618, Toolmoz 7.361815132986704APR, effective annual (UK and EU convention) expected 7.6154, Toolmoz 7.615365400572549
- Where the expected answer comes from
- Payments of 304.2194 for 36 months with 9,800 received: a separate bisection gives a monthly rate of 0.613485%, so 7.3618% nominal and 7.6154% effective; total cost = 36 × 304.21937 + 200 − 10000 = 1,151.8975
- Allowed difference
- ±0.002 absolute
Case 3
- Inputs
- Loan amount 5000Interest rate (% a year, nominal) 0Term (months) 10Upfront fee, taken from the amount you receive 0Monthly account fee, added to every payment 0
- Expected, and what Toolmoz gave
- Monthly loan payment expected 500, Toolmoz 500Total cost of credit (interest and fees) expected 0, Toolmoz 0APR, nominal (monthly rate × 12, US convention) expected 0, Toolmoz 2.945456079178636e-88
- Where the expected answer comes from
- An interest-free loan of 5,000 over 10 months costs 500 a month and nothing extra
- Allowed difference
- ±1e-9 absolute
What this shows: the engine reproduces independently worked values for these cases. It does not prove every possible input is right. To test an answer you were given, see how to check a number; to see what is and is not checked across Toolmoz, see the accuracy ledger.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Loan amount
- 10000
- Interest rate (% a year, nominal)
- 6
- Term (months)
- 36
- Upfront fee, taken from the amount you receive
- 200
- Monthly account fee, added to every payment
- 0
Example result
- Monthly loan payment
- 304.22
- Total monthly outgoing (with any monthly fee)
- 304.22
- Total repaid over the term
- 10951.90
- Total cost of credit (interest and fees)
- 1151.90
- Amount you receive after the upfront fee
- 9800.00
- Monthly rate that equates payments and amount received
- 0.613485%
- APR, nominal (monthly rate × 12, US convention)
- 7.3618%
- APR, effective annual (UK and EU convention)
- 7.6154%
The APR is the rate at which the present value of every payment equals the amount you actually receive, so upfront and monthly fees raise it above the interest rate. The UK and EU figure (Consumer Credit Directive, Annex I) is the effective annual rate; the US Truth in Lending figure multiplies the monthly rate by 12. Assumes level monthly payments in arrears, no early repayment, and equal months of one-twelfth of a year.