APR Calculator – The True Cost of a Loan, Fees Included
A loan's interest rate is not its cost. Origination fees, discount points, processing fees and monthly account charges all come out of your pocket too. The annual percentage rate (APR) folds those costs into one yearly rate, so you can compare loans with different fee structures on equal terms. This APR calculator works it out for a loan with fees, for a quote where you only know the payment, and for short-term loans repaid in one go.
APR vs interest rate: a worked example
Take a $300,000 mortgage at 6.5% over 30 years. The monthly payment is $1,896.20. The lender also charges a $1,500 origination fee and one discount point ($3,000). You pay interest on the full $300,000, but after those fees you only get the use of $295,500, the amount financed. The rate at which 360 payments of $1,896.20 are worth exactly $295,500 is 6.646%. That's the APR, 0.146 points above the quoted rate.
How the APR equation works
The APR is the rate that makes your payments, discounted back to today, equal the money you actually receive:
Amount financed = Σ payment × (1 + i)^−k
Here i is the rate per payment period. There's no closed-form answer, so the calculator finds i numerically, then annualises it. This is the actuarial method US and European rules use for evenly spaced payments.
Which fees count, and why it differs by country
In the US, the Truth in Lending Act counts interest, points, origination and broker fees and lender-required insurance. For home loans it leaves out third-party costs such as appraisal, title insurance and recording fees. UK and EU rules (the APRC) count the total cost of credit known to the lender. Indian lenders show an APR on the Key Facts Statement that includes the fees and charges they recover from you. That's why the calculator lets you tick each fee in or out: match the list your lender used.
Nominal vs effective APR, and APY
A nominal APR multiplies the periodic rate by the number of payments a year: i × 12 for monthly payments. US lenders disclose this figure. An effective APR compounds it instead: (1 + i)^12 − 1. UK and EU lenders disclose this one, and it's higher whenever there is more than one payment a year. For the mortgage above, 6.646% nominal is 6.852% effective. The same compounding step turns a savings rate into an APY.
Why APR assumes you keep the loan to the end
The disclosed APR spreads the upfront fees over the whole term. Most mortgages are refinanced or paid off with a sale long before 30 years. Pay the example loan off after 5 years and the same $4,500 of fees is spread over 60 payments, so the APR rises to 6.865%. After one year it's 8.074%. The early-payoff chart shows this curve for your loan, including any prepayment penalty.
Flat-rate quotes and payday loans
Some lenders quote a flat (add-on) rate, charging interest on the full amount for the whole term. 36 monthly payments of $350 on a $10,000 loan is a flat 8.667%, but because you repay steadily the APR is 15.682%. Use the "I know the payment" mode for these, and for car finance with a final balloon payment.
Short-term loans look cheap per loan and expensive per year. A fee of $15 per $100 for 14 days is 15% for two weeks. There are about 26 such periods in a year, so the nominal APR is 391%. If each fee were added to the balance instead, the effective rate would be about 3,724%.
What this calculator doesn't cover
- An irregular first payment period or exact day counts.
- Variable-rate and adjustable-rate loans, and credit-card (revolving) APRs.
- Monthly mortgage insurance that stops partway through the loan; the recurring charge here runs for the whole term.
- Comparing several loans side by side, or a full amortisation schedule (use the Loan EMI Calculator for that).
- Tax effects such as deductible mortgage interest.