APR calculator
Two mortgages at 5% and 5.2% look like an easy choice until the fees appear: 4,000 on the first and nothing on the second. On a 200,000 loan over thirty years, the fee pushes the first to an effective 5.19% — and the "worse" headline rate is now the better deal. APR exists precisely so that comparison can be made in one number, which is why it is the figure lenders are required to disclose.
APR calculation rules differ between jurisdictions in which fees must be included. This uses the general approach of solving for the rate that equates the payment to the net amount advanced.
APR is the rate that makes the payment on the amount you actually receive equal the payment you are charged. A 200,000 loan at 5% with 4,000 of fees has an APR of about 5.19% — the fees add nearly a fifth of a percentage point.
How to calculate APR
APR folds fees into a rate by asking what interest rate, with no fees, would produce the same payments on the money you actually walked away with. The answer depends on the term, which is the subtlety most people miss: the same fee spread over thirty years adds far less to APR than over five. That is why a low-fee, higher-rate deal often wins on a long mortgage and loses on a short personal loan, and why comparing APRs across different terms is not quite the like-for-like it appears to be.
Questions
The annual percentage rate — interest plus compulsory fees expressed as a single yearly rate.