Car Loan Calculator

Vehicle total cost with tax

taxedPrice = vehiclePrice × (1 + salesTax%)

= $28,000 × (1 + 8%)

= $30,240 ($2,240 in sales tax)

Sales tax in most states applies to the full vehicle price before trade-in or down payment. On a $28,000 car, 8% tax adds $2,240 — a cost often overlooked when budgeting.

Standard US vehicle sales tax treatment — applied to vehicle price, then reduced by trade-in/down

Loan amount

loan = taxedPrice − downPayment − tradeIn

= $30,240 − $5,000 − $0

= $25,240

Your down payment and trade-in reduce the financed amount — every dollar here saves 7.5% in annual interest. Your $5,000 in down + trade-in saves approximately $1,875 in interest over the loan term.

Monthly rate

r_month = APR / 12

= 7.5% / 12

= 0.6250%/month

APR (Annual Percentage Rate) is divided by 12 to get the monthly rate applied to your outstanding balance. At 7.5% APR, your effective monthly rate is 0.6250% — slightly different from the daily rate used in some loan structures.

FTC Truth in Lending Act (TILA) — Regulation Z APR disclosure

Monthly payment (PMT formula)

PMT = P × r / (1 − (1 + r)^−n)

P = $25,240, r = 0.6250%/mo, n = 60 mo

= $505.76/month

This is the standard loan amortization formula — each payment covers that month's interest charge, with the remainder reducing principal. Early payments are mostly interest; later payments are mostly principal.

Time value of money annuity formula — Brealey, Myers & Allen; standard amortization (Wikipedia, Khan Academy)

Month 1 interest vs principal split

M1_interest = loanAmount × r_month

= $25,240 × 0.6250% = $157.75

= $157.75 interest · $348.01 principal (31.2% of first payment is interest)

In month 1, 31.2% of your payment is pure interest cost. That interest portion decreases each month as you pay down the balance — this is front-loading, the most expensive part of any amortizing loan.

Total paid and total interest

totalPaid = PMT × months · totalInterest = totalPaid − loan

= $505.76 × 60 − $25,240

= $30,345 total paid · $5,105 interest (20.2% of loan)

You pay $5,105 in interest — 20.2% of the original loan amount — in addition to repaying the $25,240 principal. This is the cost of borrowing money over 5 years at 7.5% APR.

Effective out-of-pocket cost

effectiveCost = totalPaid + downPayment

= $30,345 + $5,000

= $35,345

Your true cost of the vehicle is $35,345 — not $28,000. The $7,345 difference represents sales tax, interest, and financing costs. This is the number that matters when comparing buying vs. leasing vs. buying used.

Loan payoff midpoint

midpoint = month where cumulative principal = 50% of loan

= month 33 of 60

= You owe 50% of principal after month 33 (2.8 years)

Due to front-loaded interest, it takes until month 33 — more than halfway through the loan — before you've paid off half the principal. This is why selling or trading in early often leaves you "underwater" (owing more than the car is worth).

36-month payoff comparison

PMT_36 = loan × r / (1 − (1 + r)^−36)

= $25,240 × 0.6250% / (1 − (1 + 0.6250%)^−36)

= $785.12/mo · saves $2,081 in interest vs 60-month

Shortening to 36 months raises your payment by $279.36/mo but eliminates $2,081 in total interest. If you can afford the higher payment, shorter terms always win on total cost.

Cost per mile (estimated)

cost/mile = effectiveCost / (12,000 mi/yr × termYears)

= $35,345 / 60,000 miles

= $0.59/mile financing cost over 5-year loan

At 12,000 miles/year, your financing cost alone runs $0.59/mile — before gas, insurance, maintenance, or depreciation. This is useful when comparing total vehicle cost with alternatives like ride-sharing or leasing.

Down payment opportunity cost

opp_cost = downPayment × ((1 + 7%/12)^n − 1)

= $5,000 × ((1 + 0.583%/mo)^60 − 1)

= $2,088 forgone if down payment were invested at 7%

Your $5,000 down payment, if invested in index funds at 7% annual return, would grow by $2,088 over the loan term. This doesn't mean you shouldn't put money down — the interest savings often exceed the opportunity cost — but it's worth knowing the true comparison.