Interest Rate Calculator

There is no closed-form formula that solves directly for a rate, so the calculator searches for it instead. It tests candidate values of i with bisection, narrowing in on the one that makes the cash price equal the present value of the payments: price = payment × (1 − (1 + i)^−n) ÷ i. After 200 narrowing steps the estimate is accurate to many decimal places. If the total of payments equals the cash price exactly, the search returns zero — the plan is genuinely interest-free.

A store offering a cash discount is, by construction, also offering financing that is not free: choosing the installment plan means giving up the discount, and giving up a discount to pay later is what interest *is*, whether or not the word appears on the contract. Comparing the cash price against the total of the payments — which is exactly what this calculator does in reverse — turns that hidden cost into a number you can put next to any other rate you are offered.

A promotional plan can be genuinely rate-free and still not be the cheapest way to buy something. Retailers and dealers sometimes price the same item higher for buyers who take the promotional financing than for buyers who pay cash or negotiate a separate cash price — the financing cost, in that case, is folded into the price rather than stated as a rate. This calculator cannot see that: it only compares the price and payments you enter. Asking directly whether a cash or negotiated price is available, and running both numbers through here, is the only way to catch a markup disguised as a 0% offer.

A small monthly rate compounds into a noticeably larger annual one: the effective annual rate is (1 + i)^12 − 1, so 2% a month works out to about 27% a year, not the 24% a straight multiplication would suggest. Comparing offers on the annual, compounded figure — never the bare monthly percentage — is what keeps the comparison honest. "Hidden" here just means *unstated*, not *deliberately concealed*: a payment plan structured as "$100 a month for 12 months" never claims to be interest-free, but it also never says what rate it implies. This calculator exists to make that implicit number explicit.

The calculation assumes a standard schedule: equal payments, one per month, starting one month after the amount is financed, with no fees folded into the payment. Real financing can differ — a down payment, a balloon payment, an origination fee, insurance add-ons, or payments that start immediately rather than after a month all shift the true rate away from what this simple model returns. Use the result to sanity-check an offer and to compare it against other financing, not as a substitute for the lender's own required rate disclosure.