Car Payment Calculator

An auto loan payment comes from the standard annuity formula, M equals P times r times (1+r) to the power n, divided by (1+r) to the power n minus 1, where r is the periodic rate and n the number of periods. The formula solves for the constant payment whose present value equals the principal, which is why each instalment splits between interest on the outstanding balance and principal reduction, with the interest share largest at the start. What distinguishes an auto loan from a generic loan is the construction of P. It is not the sticker price: it is vehicle price plus sales tax plus documentation, title and registration fees, minus the cash down payment and minus any trade-in allowance. In most US states the trade-in reduces the taxable base, so a trade worth 8,000 dollars in a 7 percent tax state saves 560 dollars in tax on top of reducing the amount financed. Practical ranges: as of recent Federal Reserve G.19 reporting, new-car rates for prime borrowers have run in the mid single digits, with subprime tiers often above 15 percent. Terms have lengthened considerably, with 72 and 84 month contracts now common. That lengthening is the main hazard the calculator exposes. Interest paid rises steeply with term while the vehicle depreciates on its own schedule, so a long loan with a small down payment leaves the borrower with negative equity, owing more than the collateral is worth, for much of the contract. The bi-weekly figure shown assumes 26 half-payments per year, equal to 13 monthly payments, with the extra amount applied to principal. Some lenders hold half-payments until a full instalment is due, in which case the modelled saving does not materialise.

Instalment credit for cars was invented because early automobiles cost more than a typical annual wage and manufacturers could not sell them for cash. The General Motors Acceptance Corporation, established in 1919, was the first large captive finance company and made monthly payment purchasing a mass-market practice; Ford resisted with the cash-based Weekly Purchase Plan of 1923 before creating Ford Credit in 1959. By the late 1920s a majority of new cars in the United States were bought on time. The mathematics is far older than the industry: compound interest annuity formulas were tabulated by mathematicians including Edmond Halley and Abraham de Moivre in the seventeenth and eighteenth centuries for life annuity pricing, and were adapted directly to instalment lending. What changed in the twentieth century was disclosure rather than arithmetic. Lenders commonly quoted add-on interest, which understated the true cost because it charged interest on the original balance rather than the declining one. The Truth in Lending Act of 1968, implemented through Regulation Z, required a standardized annual percentage rate and finance charge disclosure, forcing quotes onto the actuarial basis this calculator uses. Typical new-car loan terms have stretched from around 36 months in the 1970s to 60 months by the 1990s and beyond 68 months on average today, as rising transaction prices pushed lenders to preserve affordable monthly payments.