Installment Interest Calculator - Cash vs Monthly Payments
Reveal the effective monthly rate hidden in fixed installments, with down payment, upfront fee and first-payment timing.
Compare a real offer
Example: 750 cash or 10 payments of 86. Replace with the seller's quoted amounts.
Interest hidden in the installments
Formula and timing
Cash price − down payment − fee paid today = sum of each payment ÷ (1 + monthly rate)^k, where k is 1…N if the first payment is next month, or 0…N−1 if it is today. We solve the monthly rate numerically. Effective annual rate = (1 + monthly rate)^12 − 1.
This is an implied rate from the amounts entered, not the regulated total effective cost (CET/APR). Taxes, insurance, changing payments, dates other than monthly and undisclosed charges are not modeled. A price difference percentage is not the monthly interest rate.
Banco Central do Brasil — metodologia · Microsoft RATE · Banco Central — CET
How to find the interest rate hidden in installments
- Enter the seller's cash price, any down payment and a fee paid immediately. Add the number and amount of equal monthly installments.
- Choose whether the first installment is due today or in one month. Timing matters: a payment today has no month of interest before it.
- Read the effective monthly and annual rates, total paid and the difference from the cash price. A negative rate describes an implicit discount, not a financing charge.
- Check the displayed equation and the offer's actual schedule. This calculator does not compute a regulated CET/APR when other charges or changing due dates apply.
Installment interest questions
Why can a 'no interest' offer have a positive rate?
If the cash price is lower than the installment total, paying later has an implicit financing cost relative to that cash offer.
Why does paying the first installment today change the rate?
That payment is made without waiting a month. The remaining installments must explain the same cash-price difference over fewer future periods.
Is this the lender's disclosed APR or CET?
No. A regulated total cost can include taxes, insurance, fees and exact cash-flow dates. Ask for the official disclosure when relevant.