The Auto Loan Payment Formula
M = P × [r(1+r)^n] / [(1+r)^n − 1] where M = monthly payment, P = loan amount, r = monthly interest rate (annual rate ÷ 12), n = total number of payments (months). This is identical to the mortgage amortization formula.
📊Worked Example: $28,000 at 7.5% for 60 Months
P = $28,000. r = 7.5%/12 = 0.00625. n = 60. M = 28,000 × [0.00625 × (1.00625)^60] / [(1.00625)^60 − 1] = 28,000 × [0.00625 × 1.4536] / [1.4536 − 1] = 28,000 × 0.009085 / 0.4536 = 28,000 × 0.02003 = $560.84/month.
Amortization: How Each Payment Splits
Auto loan amortization — $28,000 at 7.5%, 60 months
| Month | Payment | Interest Portion | Principal Portion | Remaining Balance |
|---|---|---|---|---|
| 1 | $561 | $175 | $386 | $27,614 |
| 12 | $561 | $158 | $403 | $24,932 |
| 24 | $561 | $133 | $428 | $21,054 |
| 36 | $561 | $107 | $454 | $16,826 |
| 48 | $561 | $78 | $483 | $12,196 |
| 60 | $561 | $3 | $558 | $0 |
How Changing Rate and Term Affects the Formula
Sensitivity of auto loan cost to rate and term changes — $28,000 loan baseline
| Scenario | Monthly Payment | Total Interest Paid | Change vs. Baseline |
|---|---|---|---|
| $28K, 7.5%, 60mo (baseline) | $561 | $5,660 | — |
| Same but 48 months | $678 | $4,544 | -$1,116 interest saved |
| Same but 72 months | $487 | $7,064 | +$1,404 more interest |
| Rate 9.5%, same term | $587 | $7,220 | +$1,560 more interest |
| Rate 5.5%, same term | $536 | $3,160 | -$2,500 interest saved |
See the Formula at Work for Your Numbers
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