how to calculate the interest hidden in installments
To know how much interest an installment plan hides, you need the rate that equates the amount financed to the present value of the installments. There is no closed formula for several payments, so the calculation uses successive approximations. The tool below does that and shows the rate per month and per year.
The total paid is R$ 1,100, R$ 100 more, and the monthly rate is nearly 1.8%.
Paying the first installment on the spot lowers the outstanding balance and raises the rate by almost half a point a month.
Installments that look small add up to R$ 1,164: R$ 164 of interest on R$ 1,000.
With a single installment the rate is P / F - 1; the annual one comes from 1.02 to the power 12.
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.
No. Interest compounds, so the effective annual rate is (1 + i)^12 - 1. For 1.77% a month, 12 times gives 21.3%, but the correct figure is 23.46% a year.
Because you hand part of the money back before having had it for a month. The real outstanding balance is smaller, so the same sum of installments represents a higher rate.
Only when there are no fees, insurance or taxes. The CET adds up every cost of the operation, while the hidden rate considers only the difference between the cash price and the installment total on the given dates.
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.