How do you work out the interest rate from a monthly payment?

You can't — not from the payment alone. To find an interest rate you need three numbers: how much you're borrowing, the monthly payment, and how many payments there are. Give up any one of those and the answer isn't hard to compute, it's impossible.

That's not a technicality. It's the reason a quote can be perfectly true and still tell you nothing. Enter what you were told below and see every term at once.

Why there's no neat formula

A loan has four values — amount, rate, term, payment — tied together by one equation. Fix any three and the fourth follows. So finding the rate is possible in principle the moment you have the other three.

The awkward part is that the rate sits inside an exponent in that equation, and there's no way to rearrange it so the rate ends up alone on one side. Amount, payment and term can each be isolated with ordinary algebra. The rate can't.

So it's found by searching instead: guess a rate, compute what payment it would produce, and compare. Too high, guess lower. Too low, guess higher. Repeat until the computed payment matches the quoted one to the penny. Every financial calculator ever built does this — a spreadsheet's RATE() function does it, and so does the decoder above. It just happens in a few thousandths of a second.

The check you can do in your head

Most of the time you don't actually need the rate. You need to know whether the loan is expensive, and that's two pieces of arithmetic:

1. Payment × number of payments = total paid.
2. Total paid − amount borrowed = the cost of the loan.

$450 a month for 60 months is $27,000. Borrow $20,000 and the loan costs you $7,000 — thirty-five cents of interest for every dollar you borrowed. You now know enough to decide, and you did it without knowing the rate at all.

If the total paid is less than the amount borrowed, the quote is wrong. No lender pays you to take their money — so either the term is longer than you were told, or there's a balloon payment at the end.

Rate, APR, and which one to ask for

Solving from a payment gives you the interest rate — the price of the money itself. The APR is that plus the fees, expressed as a yearly rate, and it is the number designed for comparing two offers against each other.

Whenever there are origination or processing charges, the APR is higher than the rate you'd solve from the payment. That gap is the fees, and it is exactly why the APR is the number to ask for. Under federal Truth in Lending rules a lender must disclose the APR and the total of payments in writing before you sign — which means you never have to reverse-engineer anything if you simply ask.

What to do with the number once you have it

A rate is only meaningful next to another one. Get a quote from a credit union or your own bank and compare — the full decoder has a field for that second rate and prices both loans side by side, so the difference arrives in dollars rather than percentage points.

And if the two quotes are close, the tiebreaker usually isn't the rate. It's whether there's a prepayment penalty, and whether the interest is precomputed — because if it is, paying the loan off early saves you almost nothing, and every “I'll just pay it off faster” plan you had quietly stops working.