Car loan calculator
A car loan is an ordinary amortising loan; the complication is only in what gets financed.
%
%
years
Monthly payment
611.71
- Amount financed
- 30 240.00
- Sales tax
- 2240.00
- Total interest
- 6462.72
- Total of payments
- 36 702.72
Show the working
- Vehicle price = 32 000
- Deposit = 4000
- Trade-in value = 0
- Sales tax = 7
- Annual interest rate = 7.9
- Term = 5
- taxable = max(32 000 - 0, 0) = 32 000
- Sales tax = 32 000 * 7 / 100 = 2240
- Amount financed = max(32 000 + 2240 - 4000 - 0, 0) = 30 240
- i = 7.9 / 100 / 12 = 0.006 583 33
- n = 5 * 12 = 60
- growth = (1 + 0.006 583 33)^60 = 1.482 46
- Monthly payment = 0.006 583 33 == 0 ? 30 240 / 60 : 30 240 * 0.006 583 33 * 1.482 46 / (1.482 46 - 1) = 611.712
- Total of payments = 611.712 * 60 = 36 702.7
- Total interest = 36 702.7 - 30 240 = 6462.72
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- amount financed = price + sales tax - deposit - trade-in
- payment = P i (1+i)^n / ((1+i)^n - 1)
Many US states charge sales tax on the price net of trade-in, which is what this assumes. Some tax the full price.
This is arithmetic, not financial advice. Real products carry fees, tax treatment and terms that no formula captures.