Quick answer
APR is the rate i for which the payments repay the loan amount minus upfront fees, quoted as 12 × i. A $200,000 loan at a 6% note rate with $4,000 of fees and a 30-year term has an APR of 6.1895%, with a monthly payment of $1,199.10.
Enter the loan amount, fees, note rate and term. The calculator returns the APR and the payment.
Related tools: Amortization Calculator: Full amortization schedule with optional extra monthly payments. Refinance Calculator: Monthly savings and break-even time from refinancing. Loan Calculator: Estimate your monthly loan payment, total interest and total cost.
How to use the APR Calculator
- Enter loan amount ($) (above 0).
- Enter upfront fees ($) (0 or more).
- Enter note rate (%) (between 0 and 100).
- Enter term (years) (between 0 and 50). It starts at 30.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Loan amount | A number, in $ | > 0 |
| Upfront fees | A number, in $ | ≥ 0 |
| Note rate | A number, in % | ≥ 0, ≤ 100 |
| Term | A number, in years | > 0, ≤ 50, starts at 30 |
Formula and method
Formula
Find i such that payment × (1 − (1 + i)^−n) ÷ i = amount − fees; APR = 12 × i
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
The payment is set by the note rate on the full amount; the APR is the rate that equates the payments to the amount you actually receive.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Loan amount = 200000; Upfront fees = 4000; Note rate = 6; Term = 30.
| Result | Value |
|---|---|
| APR | 6.1895% |
| Monthly payment | $1,199.10 |
Example 2
Inputs: Loan amount = 10000; Upfront fees = 500; Note rate = 7; Term = 5.
| Result | Value |
|---|---|
| APR | 9.1749% |
| Monthly payment | $198.01 |
Example 3
Inputs: Loan amount = 50000; Upfront fees = 0; Note rate = 4; Term = 10.
| Result | Value |
|---|---|
| APR | 4% |
| Monthly payment | $506.23 |
The first line is the headline result (aPR). Below it the aPR Calculator lists monthly payment, which describe the same case from other angles. IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Why APR exceeds the note rate
The borrower receives $196,000 but repays on $200,000, so the effective cost is higher than the 6% nominal rate. APR folds the fees into one comparable rate. With zero fees APR equals the note rate.
Comparing offers
APR makes loans with different fees comparable, assuming you keep the loan for the full term. If you sell or refinance early, the fees are spread over fewer months and the true cost is higher. Fees must be less than the loan amount.
How the result changes with loan amount
Holding every other input at the first worked example, this table changes only loan amount. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Loan amount | APR | Monthly payment |
|---|---|---|
| 100000 | 6.3851% | $599.55 |
| 200000 | 6.1895% | $1,199.10 |
| 400000 | 6.094% | $2,398.20 |
| 800000 | 6.0468% | $4,796.40 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Upfront fees: entering "1000" shows "Fees must be less than the loan amount." beside that field and no result.
- Loan amount: entering "0" shows "Loan amount must be greater than 0." beside that field and no result.
Choosing between the APR Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Amortization Calculator](/finance/amortization-calculator/) | loan amount, interest rate and term | Monthly payment |
| [Refinance Calculator](/finance/refinance-calculator/) | current balance, current rate and current remaining term | Monthly savings |
| [Loan Calculator](/finance/loan-calculator/) | loan amount, interest rate and term | Monthly payment |
| [Down Payment Calculator](/real-estate/down-payment-calculator/) | home price and down payment | Down payment |
| [Auto Loan Calculator](/finance/auto-loan-calculator/) | vehicle price, down payment and interest rate | Monthly payment |
Background: loans and mortgages
The interest rate is the cost of borrowing the principal; the APR also folds in certain fees, so a lower rate with high fees can have a worse APR. These calculators use the rate you enter and do not add fees, insurance or taxes, so add fees to the principal if you want to include them.
A fixed-rate loan is paid in equal instalments, early ones mostly interest. Extra payments go straight to principal, which shortens the loan and cuts interest; adjustable rates, escrow changes and prepayment penalties are not modelled.
Assumptions and limitations
- Zero fees give APR = note rate
- Fees must be less than the loan amount
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for upfront fees and loan amount to confirm this.
Frequently asked questions
Is APR the same as interest rate?
No, APR includes fees.
Does APR include insurance?
Only if the lender counts it as a finance charge.
Which should I compare?
Compare APRs for loans of the same term.
What does the APR Calculator calculate?
Annual percentage rate of a loan once upfront fees are counted. It returns APR and Monthly payment.
What formula does the APR Calculator use?
Find i such that payment × (1 − (1 + i)^−n) ÷ i = amount − fees; APR = 12 × i. The payment is set by the note rate on the full amount; the APR is the rate that equates the payments to the amount you actually receive.
What do I need to enter in the aPR Calculator?
You enter Loan amount ($), Upfront fees ($), Note rate (%) and Term (years).
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. Zero fees give APR = note rate.
What are the limits of this calculator?
Zero fees give APR = note rate. Fees must be less than the loan amount.
What is an example of a aPR result?
With loan amount 200000, upfront fees 4000, note rate 6 and term 30, the aPR is 6.1895%.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: Zero fees give APR = note rate.
Related calculators
- Amortization Calculator — Full amortization schedule with optional extra monthly payments.
- Refinance Calculator — Monthly savings and break-even time from refinancing.
- Loan Calculator — Estimate your monthly loan payment, total interest and total cost.
- Down Payment Calculator — Down payment amount and loan size from a percentage.
- Auto Loan Calculator — Monthly car payment after down payment and trade-in.
- Interest Rate Calculator — Annual interest rate implied by a loan amount, payment and term.
- HELOC Calculator — Interest-only draw-period payment and the repayment-period payment of a home equity line.
- Cash Back or Low Interest Calculator — Compare a cash rebate with a lower financing rate on a purchase.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.