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APR Calculator: The True Annual Cost of a Loan
The interest rate alone understates what a loan costs when there are fees. Enter the amount, rate, term and upfront fees to see the annual percentage rate that reflects what you actually receive and repay.
The idea behind APR
Two loans can carry the same interest rate and still cost different amounts. Suppose one lender takes 600 off the top before handing you the money. You repay the full face value, but you receive less. The annual percentage rate fixes that by treating the cash received as the amount borrowed and finding the rate that makes your actual payments repay it.
Mathematically it is the internal rate of return of the loan from the borrower's side. The monthly rate r solves Net = Payment × (1 − (1 + r)−n) ÷ r, where Net is the amount after fees. As with the interest rate calculator, this has no closed form, so bisection narrows in on it.
Using APR to compare offers
Compare loans of the same type and similar length by APR rather than by the stated rate. A loan with a lower stated rate and a large fee can have a higher APR than one with a higher rate and no fee. APR also depends on how long you keep the loan, because fees are spread over the term. If you repay early, the fee is spread over fewer months and the real cost of the loan rises.
- Check which charges the lender includes. Late fees and optional insurance are usually left out.
- For loans of different lengths, look at the total cost of credit as well.
- For a payment-based view of a single loan, use the loan calculator.
APR, APY and nominal rates
The APR shown here is a nominal rate: twelve times the monthly rate. Some regions define APR on a different compounding basis or require specific fees to be included, so the lender's disclosed APR may differ slightly from this result. The effective annual rate adds the effect of monthly compounding and is closer to what a savings account would call its yield. When comparing with a deposit rate, use the effective figure.
Limits
This calculator assumes level monthly payments on a fixed rate and a single set of fees paid at the start. It does not model monthly account fees, balloon payments, variable rates or optional insurance. Enter fees that reduce the proceeds; fees that you pay separately in cash have the same effect on cost and can be entered the same way. Results are estimates for comparison and not a legal disclosure.
As a worked check, take a one-month loan of 1,000 at a stated 12% (1% for the month) with a fee of 10. You repay 1,010 but receive 990, so the monthly cost is 1,010 ÷ 990 − 1, or about 2.02%, which is an APR of about 24.2%. A fee that looks small beside the loan can therefore double the real annual cost when the loan is short. The same fee on a longer loan is spread across many months and has a much smaller effect.
Worked example
A 20,000 loan at a stated 9% over 60 months, with 600 of fees taken out of the proceeds.
Inputs
| Loan amount (the face value you repay) | 20000 |
|---|---|
| Stated annual interest rate | 9 % |
| Number of monthly payments | 60 |
| Fees deducted from the loan at the start | 600 |
Result
Compared with the stated rate of 9.000%.
| Monthly payment | 415.17 |
|---|---|
| Cash you actually receive | 19,400.00 |
| Total of all payments | 24,910.03 |
| Total cost of credit (payments minus cash received) | 5,510.03 |
| Effective annual rate (compounded) | 10.812% |
| Gap between APR and stated rate | 1.311 percentage points |
- APR is the rate that makes the present value of your payments equal the cash you actually received. Rules for what counts as a fee differ by country, so use the lender's disclosed APR for legal comparison.
Financial disclaimer: Results are estimates for planning and education. They are not financial, tax or legal advice. Fees, taxes, rates and rules vary by lender, product and country, so confirm figures with your provider or a qualified adviser before making decisions.
Frequently asked questions
What is APR on a loan?
It is the yearly cost of borrowing expressed as a rate, including interest and certain fees, based on the cash you actually receive.
Why is my APR higher than the interest rate?
Because fees reduce the cash you receive while you still repay the full amount. The same payments on less money means a higher effective rate.
Is a lower APR always the better loan?
Usually, for similar loans. Also compare the total cost of credit, the term and any penalties for early repayment.
Does APR include late fees?
Typically not. APR covers charges that every borrower pays to get the loan; conditional charges such as late fees are normally excluded.
What if there are no fees?
Then the APR equals the stated rate, which is a quick way to verify the calculation.
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References and sources
- Consumer Financial Protection Bureau: explanations of APR and the cost of credit. Link
- Internal rate of return as defined in introductory corporate finance texts.