Installments or Cash? Which Is Cheaper

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interest-free installments worth it black friday

Black Friday: are interest-free installments worth it? The value in today's money

Paying in interest-free installments does not change the total you pay, but it changes what that total is worth today: R$ 100.00 five months from now costs less than R$ 100.00 right now for someone whose money earns interest. On Black Friday that adds to the offer's discount, and the tool shows the result in today's reais.

How installments enter the discount math

The method is present value: each installment is discounted by the yield the money would earn until its payment date, and the sum of those installments brought to today is the real cost of the installment plan. With 10 installments of R$ 100.00, the first in 30 days and a yield of 1% a month, the cost today is R$ 947.13, not R$ 1,000.00. If the first installment is paid right away, it rises to R$ 956.60.
Tying this to Black Friday, the real discount in present value is 1 − cost today ÷ earlier price. For a product that cost R$ 1,000.00 and now sells for R$ 1,000.00 in 10 interest-free installments, there is no discount on the tag, but in present value the installment plan costs 5.29% less. It is a gain that only exists if the money is really earning interest, and the yield used is an assumption of yours, chosen in the tool panel.
Two cautions. First, the yield: the lower it is, the smaller the gain (at 0% a month, the present value equals the total). Second, the plan is only “interest-free” if the sum of the installments equals the cash price; when the store gives a discount for paying in cash, the hidden interest shows up in the Cash discount mode of the same tool. The tool compares only the values you type and has no price history.

What the installment plan is worth today

10 x R$ 100.00, first in 30 days

Input: R$ 1.000,00 em 10x sem juros; rendimento 1% ao mês; antes R$ 1.000,00
Expected output: Custo hoje R$ 947,13; desconto real 5,29%

Sum of 100 ÷ 1.01^k for k from 1 to 10.

Same plan, first installment at once

Input: R$ 1.000,00 em 10x sem juros; 1ª no ato; rendimento 1% ao mês
Expected output: Custo hoje R$ 956,60; desconto real 4,34%

The first installment earns nothing, so the gain drops.

12 x R$ 100.00 at 1% a month

Input: R$ 1.200,00 em 12x sem juros; 1ª em 30 dias; antes R$ 1.200,00
Expected output: Custo hoje R$ 1.125,51; desconto real 6,21%

More installments give a larger gain, because the last ones weigh less in present value.

The yield drops to 0.5% a month

Input: R$ 1.200,00 em 12x sem juros; 1ª em 30 dias; antes R$ 1.200,00
Expected output: Custo hoje R$ 1.161,89; desconto real 3,18%

With half the yield, the installment gain drops to about half.

Full tool FAQ

How do I know whether installments or cash is better?

Compare the cash price with the cost of the installments in today's money. To do that, work out how much would have to be invested today to pay each installment on its date, considering the yield and income tax. If that total is below the cash price, installments win; if it is above, cash wins. The Worth it mode does this and shows the difference in reais.

What is the interest rate hidden in an installment plan?

Are 10 interest-free installments really interest-free?

Does paying the first installment upfront or in 30 days change the rate?

Which yield rate should I use?

Is income tax part of the calculation?

What is the difference between the hidden rate and the CET?

What is the break-even?

What if the installments add up to less than cash?

Can I share my simulation?

Frequently asked questions

Are interest-free installments on Black Friday worth more than a cash discount?

It depends on the cash discount and on your money's yield. Compare in the Cash discount mode: it shows the monthly rate that the discount reveals, and if it is lower than your yield, installments pay off.

Which yield should I use?

The one where your money would actually sit: savings, CDB, LCI/LCA or another. The tool offers ready options and lets you type your own, before or after income tax, depending on the tax choice.

What if the card hits its limit or I use revolving credit?

Then the math changes: revolving-credit interest or any late fee is not in this tool and cancels the installment gain. Use the Embedded interest mode if any installment carries a surcharge.

Next steps

Black Friday: are interest-free installments worth it? The value in today's money

How installments enter the discount math

The method is present value: each installment is discounted by the yield the money would earn until its payment date, and the sum of those installments brought to today is the real cost of the installment plan. With 10 installments of R$ 100.00, the first in 30 days and a yield of 1% a month, the cost today is R$ 947.13, not R$ 1,000.00. If the first installment is paid right away, it rises to R$ 956.60.

Tying this to Black Friday, the real discount in present value is 1 − cost today ÷ earlier price. For a product that cost R$ 1,000.00 and now sells for R$ 1,000.00 in 10 interest-free installments, there is no discount on the tag, but in present value the installment plan costs 5.29% less. It is a gain that only exists if the money is really earning interest, and the yield used is an assumption of yours, chosen in the tool panel.

Two cautions. First, the yield: the lower it is, the smaller the gain (at 0% a month, the present value equals the total). Second, the plan is only “interest-free” if the sum of the installments equals the cash price; when the store gives a discount for paying in cash, the hidden interest shows up in the Cash discount mode of the same tool. The tool compares only the values you type and has no price history.

What the installment plan is worth today

10 x R$ 100.00, first in 30 days

Input: R$ 1.000,00 em 10x sem juros; rendimento 1% ao mês; antes R$ 1.000,00
Expected output: Custo hoje R$ 947,13; desconto real 5,29%

Sum of 100 ÷ 1.01^k for k from 1 to 10.

Same plan, first installment at once

Input: R$ 1.000,00 em 10x sem juros; 1ª no ato; rendimento 1% ao mês
Expected output: Custo hoje R$ 956,60; desconto real 4,34%

The first installment earns nothing, so the gain drops.

12 x R$ 100.00 at 1% a month

Input: R$ 1.200,00 em 12x sem juros; 1ª em 30 dias; antes R$ 1.200,00
Expected output: Custo hoje R$ 1.125,51; desconto real 6,21%

More installments give a larger gain, because the last ones weigh less in present value.

The yield drops to 0.5% a month

Input: R$ 1.200,00 em 12x sem juros; 1ª em 30 dias; antes R$ 1.200,00
Expected output: Custo hoje R$ 1.161,89; desconto real 3,18%

With half the yield, the installment gain drops to about half.

Full tool FAQ

How do I know whether installments or cash is better?

What is the interest rate hidden in an installment plan?

Are 10 interest-free installments really interest-free?

Does paying the first installment upfront or in 30 days change the rate?

Which yield rate should I use?

Is income tax part of the calculation?

What is the difference between the hidden rate and the CET?

What is the break-even?

What if the installments add up to less than cash?

Can I share my simulation?

Frequently asked questions

Are interest-free installments on Black Friday worth more than a cash discount?

Which yield should I use?

The one where your money would actually sit: savings, CDB, LCI/LCA or another. The tool offers ready options and lets you type your own, before or after income tax, depending on the tax choice.

What if the card hits its limit or I use revolving credit?

Then the math changes: revolving-credit interest or any late fee is not in this tool and cancels the installment gain. Use the Embedded interest mode if any installment carries a surcharge.