Installments or Cash? Which Is Cheaper

Installments only pay off when the hidden interest is lower than what your money would earn.

When a store says 10 interest-free installments or 5% off for cash, it is comparing money on different dates. The hidden interest rate is the monthly rate that equates the amount financed (cash price minus down payment) to the present value of the installments. Example: R$ 1,000 in cash or 10 installments of R$ 110, with the first due in 30 days, hides 1.77% a month, or 23.46% a year. The tool solves the IRR numerically, accepts a first installment upfront or in 30 days, and handles the interest-free case (zero rate) and installments that add up to less than cash (negative rate). The rate alone does not decide: you have to compare it with what your money would earn. Paying cash means giving up keeping that amount invested during the installments. The tool brings each installment to present value using the yield you choose, with income tax by the Brazilian regressive table (22.5% up to 180 days, 20% from 181 to 360, 17.5% from 361 to 720 and 15% beyond 720), a flat rate or exempt (the case of poupança savings and LCI/LCA for individuals). Poupança follows the 0.5% a month rule while the Selic is above 8.5% a year, and the reference Selic comes from Central Bank of Brazil data. An interest-free plan can be the best option. Ten installments of R$ 100 for the same R$ 1,000 product, with money earning 1% a month, cost R$ 947.13 in today's money. If cash were R$ 950, installments would still win by R$ 2.87; if it were R$ 900, cash wins by R$ 47.13. The Break-even mode shows the minimum discount and the minimum yield at which the choice flips, and the simulation shows the balance month by month. Limits that matter: the hidden rate only considers price, down payment, installments and dates. The CET of a loan also includes fees, insurance and taxes. The tool assumes a constant, risk-free yield, ignores your card limit, cash-flow flexibility and the temptation to spend the saved money, and is not financial advice.

Pick the mode, fill in price, installments and what your money earns.

1. In Hidden interest, enter the cash price, the down payment (if any), the number of installments and the value of each, and say whether the first is due upfront or in 30 days.
2. In Worth it? choose where the money would be kept (poupança, CDB, LCI/LCA or another yield) and the tax; use Break-even, Month by month, Cash discount or Compare offers to dig deeper.
3. Copy the result or the link: it carries the same values already filled in, so you can send it to whoever is deciding with you.

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Sources and references for this tool

These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.

• Lei 11.033/2004, tributação de rendimentos de renda fixaPresidência da República, Basis of the regressive income tax table (22.5% to 15%) and the LCI/LCA exemption for individuals.
• Lei 12.703/2012, remuneração da poupançaPresidência da República, Sets poupança remuneration: 0.5% a month with the Selic above 8.5% a year, or 70% of the Selic otherwise.
• Dados Abertos do Banco Central, séries do SGSBanco Central do Brasil, Source of the accumulated monthly Selic (SGS 4390) used as the yield reference.

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