Interest Rate Calculator

Because three of the four numbers in a loan pin down the fourth. The amount borrowed, the payment and the number of payments are linked to the rate by one equation — the present value of the payment stream must equal the amount advanced. There is no algebraic way to rearrange that equation for the rate, so the calculator solves it by iteration, which is exactly what Regulation Z Appendix J (b)(9)(ii) expects a computer to do.

It is the same when the loan has no fees, and lower than the APR when it does. This calculator only sees the money you repay, so it recovers the rate on the note. APR also folds in prepaid finance charges such as points and origination fees, which make the true cost of credit higher than the note rate. If you know your fees, put them into the APR calculator to get the comparable figure.

Regulation Z Appendix J (b)(1) annualises by simply multiplying the monthly rate by twelve, which ignores the fact that interest is charged twelve times a year. The effective annual rate compounds it instead. A 1% monthly rate is 12% nominal but 12.6825% effective. Loan rates in the US are quoted nominally and savings yields are quoted as compounded APYs, so comparing a loan rate against a savings APY without converting one of them is a mistake.

Only principal and interest. A mortgage payment usually also collects property tax, homeowners insurance and sometimes mortgage insurance into an escrow account; those are not repaying the loan, so including them would make the calculator report a rate far higher than the one you are actually paying. Your statement or amortisation schedule will show the principal-and-interest portion separately.

Because the payments you entered add up to less than the amount borrowed. If you borrow $6,000 and pay $200 a month for 24 months you have repaid $4,800, which no non-negative interest rate can explain — something in the inputs is wrong, usually the term or a payment that omits part of the amount due. A loan that exactly repays the principal and no more is a genuine 0% loan, and the calculator reports it as such.

The rate is solved until the bracket is narrower than one part in a quintillion, and every step is carried in decimal arithmetic rather than binary floating point. The limiting factor is your inputs, not the solver: because payments are rounded to the cent, a cent of rounding in the payment moves the recovered rate by roughly a thousandth of a percentage point. That is why the result is displayed to two decimals, the precision Regulation Z calls correct.

Yes, but enter the ORIGINAL loan amount and the ORIGINAL number of payments, not the current balance and the payments you have left. The two are only consistent at the start of the loan. Using the current balance with the remaining term also works and returns the same rate, provided the payment has never changed — but mixing an original balance with a remaining term will not.

No. It assumes a level payment that fully repays the loan over the term, which is what Appendix J calls a regular transaction with a single advance. An interest-only period, a balloon payment at the end, or a payment that steps up partway through all break that assumption. For those, the amortization calculator lets you model the schedule directly.