interest-free installments or cash discount
The rule of thumb is simple: pay cash if the discount is larger than what your money would earn during the installments, and use installments if it is smaller. Measuring that is the hard part, because the installments fall on different dates. The calculator below brings everything to today's money and gives the verdict in reais.
The 5% discount is below the 5.29% break-even, so installments come out slightly ahead.
With a 10% discount cash wins comfortably; the hidden rate is 1.96% a month.
Poupança earns less than 1% a month, so the same 5% discount becomes worth taking.
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.
It depends on the term and the yield. Over 10 installments, a 5% discount equals 0.94% a month of hidden interest (11.9% a year). If your money earns more than that, installments are better; if it earns less, take the discount. Over 10 installments the break-even at 1% a month is a 5.29% discount.
The comparison assumes you have the money and choose between spending it now or keeping it invested. If you would have to borrow to pay cash, compare the discount with the interest on that loan, which is usually far above any yield.
It does: tax lowers the net yield and favors paying cash. Poupança and LCI/LCA for individuals carry no income tax. For CDBs and Treasury bonds the regressive table applies, from 22.5% (up to 180 days) to 15% (beyond 720 days).
Enter the cash price and the installments: the tool finds the interest rate the plan hides.
That is 23.46% per year (effective rate, compounded).
Each month the plan charges 1.772% on the balance you still owe (first installment in 30 days). In total you pay R$100.00 more than the cash price.
This monthly rate is about 1.6 times the reference monthly Selic rate.
If the first installment were paid upfront, the hidden rate would be 2.184% per month (29.60% per year).
This is the rate hidden in the price difference and the dates. The CET (Total Effective Cost) of a loan also adds fees, insurance and taxes, which are not included here. If any apply, the real cost is higher.
Educational tool, not financial advice. It ignores fees, insurance, risk and your personal situation. Calculated in your browser.