How we calculate

Every number in the calculators comes from a method that is written down here. If you are about to act on a result, this is the page that says where it comes from, what it assumes and what it leaves out. The calculators themselves run in your browser, and the same engine that powers them is the one that recalculates the examples in the guides.

Money and rounding

Amounts are handled as exact decimal numbers, never as floating-point values, and each amount in a schedule is rounded to the cent. Rounding leaves tiny differences, so the last installment absorbs whatever is left: that is why a PRICE schedule can end with an installment a few cents away from the others.

Interest and amortization

Each month's interest is the opening balance times the monthly rate. Under the PRICE system the installment is constant and given by PMT = PV × i × (1 + i)^n ÷ ((1 + i)^n − 1). Under SAC the amortization is constant, PV ÷ n, and the installment falls as the interest does. A grace period either pays the interest as it comes or adds it to the balance, as you choose.

Rates and their conversions

A rate is only comparable with another if both are on the same basis, so each calculator asks for it. A nominal annual rate is divided by twelve to give the monthly rate (12% a year nominal is 1% a month). An effective annual rate is converted by i = (1 + r)^(1/12) − 1 (12% a year effective is about 0.95% a month). An effective monthly rate is used as given. Yearly figures for a monthly rate compound it twelve times, so 1% a month is 12.68% a year, not 12%. For indexes published per business day, such as the Brazilian CDI, the annual rate compounds 252 business days.

The total effective cost (CET)

The CET is the internal rate of return of the borrower's cash flow: on one side, what was actually received (the amount less the fees deducted up front), on the other, every payment, including insurance and financed charges. The rate that makes the two equal is found by bisection, a method that always converges, and it is reported as a yearly rate. With no charges it equals the contract's rate, which is a built-in check. The idea follows the Brazilian definition of the CET, but the figure is an estimate from the data you enter, not the number in a bank's contract.

Late payment charges

The penalty is the original amount times the penalty rate, charged once. The late interest is simple and proportional to the days: original amount × daily rate × days late. When the daily rate is derived from a monthly one, the conversion follows the country's day-count convention: month divided by 30, or twelve months over 365 days, or over 252 business days. Monetary correction is not part of this calculation.

The tax on credit in Brazil

For countries that have a rule, the simulation can estimate the tax on credit operations for individuals. It applies a daily rate to the principal of each installment for the days between the release of the loan and its due date, up to a legal ceiling, plus a flat rate on the operation. The figure is shown as an estimate with the rate used, and it can be added to the loan, deducted from the amount received or left out. If the contract already includes the tax among its charges, the estimate is not added a second time.

Investment returns

An offer's yield is projected over the horizon and taxed according to the product and the days held, and the ranking is by the net return, never the gross one. A share of an index is applied to the period the index is published over and only then compounded. Index levels are treated as constant over the horizon, so a projection is an estimate, not a forecast. The split of the budget is searched for the highest net return and checked against putting everything in the best offer.

Where the data comes from

• Brazilian indexes (CDI, Selic, IPCA, TR): the Central Bank of Brazil's time-series system, SGS (opens in a new tab), fetched about once a day.
• United States (SOFR): the Federal Reserve Bank of New York (opens in a new tab), fetched about once a day.
• Euro area (Euribor): the European Central Bank's data portal (opens in a new tab), fetched about once a day. EURIBOR® is a registered trademark of EMMI; see the legal notice.
• Average lending rates in Brazil: the Central Bank's open data (opens in a new tab), the rates that lenders report by credit type, refreshed about once a day. They are averages of operations already made, with taxes and operating charges, not offers.
• Average lending rates in the United States and Spain: the Federal Reserve's consumer credit release (G.19) (opens in a new tab), the annual percentage rate that commercial banks report for personal and new-car loans, surveyed once a quarter; and the European Central Bank's bank interest rate statistics (opens in a new tab), the average rate on new loans to households in Spain with a rate fixed for over a year, published monthly and without fees, insurance or taxes. Each is a single average for the whole market, not a list of lenders. The monthly and yearly effective rates shown are worked out here from the figure each one publishes, and that is the only change.
• Lists of institutions: the Central Bank of Brazil (list of participants and IF.data) and the FDIC (opens in a new tab) for the United States, refreshed about once a week. They are used only to identify an institution and imply no endorsement or ranking. There is no list for Spain yet, and the field is free text.
• Tax and penalty tables: kept by the system for each country, each rule with the date from which it applies, so a change in the law is a correction to the data and not a new release. These tables are the part to double-check against the rule in force.

What we deliberately leave out

• Loans whose rate follows an index, variable-rate mortgages, revolving credit and credit cards.
• Investments whose price moves with the market, such as funds, stocks and bonds traded before maturity.
• Your personal tax situation, other than the product tables, and any rule specific to your contract or to your lender.
• Legal, tax or financial advice: the calculators inform, they do not recommend.

How the numbers are checked

The engine is tested against figures worked out by hand, and every example number published in the guides and on the page of each calculator is recomputed by the engine itself on every release: if a text and a calculator disagree, the release does not go out. Each page shows the date it was last reviewed. A date does not mean a rule has not changed since: laws and rates change, which is why the results are estimates and the contract and the lender's statement prevail.

Corrections

If a result does not match your contract, or a rule here has changed, tell us through the contact details on the About page. We check it against the primary source and correct the data or the text, and the review date of the page changes when we do.