APR Calculator
The real annual cost of a loan once its fees are counted, and how far it sits above the advertised rate.
Recent
Formula
How the calculation works
The advertised rate is the interest rate, not the cost of the loan. Fees are paid out of the loan before it reaches you, but the payment is still set on the full amount, so you receive less and repay the same -- which lifts the true annual rate above the quoted one.
Finding it means solving for the monthly rate at which the payments, discounted back, equal what you actually received. There is no elementary formula for that, so the tool bisects until it converges, which it does to the cent. On the worked example, 3,000 of fees on a 200,000 loan at 5% moves the real rate to 5.13%.
Common mistakes
- Comparing loans on the interest rate alone. Two loans with the same rate and different fees have different APRs, and the gap grows as the term shortens.
- Assuming the APR and the interest rate should match. They only match when there are no fees at all, so any difference is the cost of the fees, spread over the term.
When to use it
- Use it to compare two loan offers that quote the same rate but different fees, which is where the advertised figure hides the difference.
- It is also the check on any quote that leads with a low rate: put the fee in and see what the loan actually costs each year.
Worked example
A 200,000 loan at 5% over 30 years with 3,000 fees: payment 1,073.64 and an APR of 5.13%.
Common questions
Why is the APR higher?
The upfront fee is taken out of the loan, but the payment is still set on the full amount. You receive less and repay more, so the real rate rises above the quoted one.
Is APR the same as EAR?
No. APR annualises the monthly compounding the way a lender discloses it, while EAR gives the true compounded rate. For comparing loans, APR is the right one.
Related tools
-
Loan Repayment (EMI)
The fixed monthly payment on a loan, and what the interest costs over the whole term.
-
Credit Card Payoff
How long a card balance takes to clear at a given monthly payment, and what it costs.
-
Break-Even Point
How many units must sell before a business covers its costs.
-
Mortgage Affordability
How large a mortgage your income supports, and which limit actually binds.
-
Total Loan Cost
What the repayments add up to, and how much of it is interest.
-
Extra Payment Saving
What paying a little extra each month saves in time and interest.