I took out a R$45,000 loan from the bank to buy a Chevrolet Onix, with installments of R$1,200 for 48 months. But when I add it all up it comes to almost R$58,000, and I don't understand what the exact formula is to figure out what interest rate they're charging me. How do I do that?
I've been through that and it's really annoying when you see the difference between what you borrowed and what you're gonna pay. The most straightforward way is to use the internal rate of return (IRR) formula or just plug the numbers into an online car financing calculator - you put in the 45,000 reais, the 48 installments of 1,200 reais, and the calculator tells you the monthly rate, which you then multiply by 12 to get the annual rate. If you want to calculate it by hand, it's actually pretty complicated because it involves an equation that you can only solve by trial and error, but honestly nobody does that - your bank should have given you a document (the proposal or contract) that makes it crystal clear what rate they're charging, so if you can't find it there, shoot them a message asking for that information in black and white.
Calculating this interest rate manually is honestly tedious, because the formula involves an equation that doesn't have a simple solution - it's the kind of thing that's only practical with a calculator or computer. But you can understand what's going on: you borrowed 45 thousand, you're going to pay 1,200 times 48 (that's 57,600), meaning you'll shell out an extra 12,600. That extra amount divided by the initial principal gives you roughly 28% total, but that's not the direct monthly or annual rate.
The less painful way is to just use a financial calculator - there are several free ones online where you enter the loan amount, the number of installments, and the value of each one, and it gives you back the rate. Search for "interest rate calculator" or "IRR". Another option is to open a spreadsheet (Excel, Calc, Sheets) and use the RATE() function, which does this calculation automatically. You put in the number of periods (48), the present value as negative (-45000), zero as the future value, and the payment (1200), and it calculates the rate per period.
If you want a quick estimate without tools, the rate should be around 2% to 2.5% per month - which comes out to something between 24% and 30% per year. But for the exact value, there's no way around the calculator, because the installments are paying off principal and interest simultaneously, and that changes every month.
Log into answer.
