Authoritative data source & methodology
Primary references:
- Consumer Financial Protection Bureau (CFPB), “Auto loans” resources & disclosures (TILA/Reg Z). consumerfinance.gov
- Federal Reserve, Truth in Lending (Regulation Z) overview for APR and amortization disclosures. federalreserve.gov
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The formula explained
Amount financed:
$\\text{OTD} = (P - T_v) \\times (1 + t) + F$
$\\text{Financed} = \\max\\{\\text{OTD} - D + T_b,\\ 0\\}$
where $P$ = price, $T_v$ = trade-in value, $t$ = tax rate (decimal), $F$ = fees, $D$ = down payment, $T_b$ = trade-in loan balance owed (negative equity).
Payment (standard amortized loan, monthly):
$i = \\dfrac{\\text{APR}}{12}$, $n = \\text{term months}$, $L = \\text{Financed}$
$\\displaystyle \\text{Payment} = \\frac{iL}{1 - (1 + i)^{-n}}$
Total interest: $\\text{TI} = n\\times\\text{Payment} - L$; Total cost: $\\text{OTD} + \\text{TI}$.
Glossary of variables
| Symbol / Field | Meaning |
|---|---|
| P (Bike Price) | Sticker sale price before taxes. |
| t (Sales Tax) | Sales tax rate as a decimal (e.g., 0.085 for 8.5%). |
| F (Fees) | Doc, title, registration, inspection, etc. |
| D (Down Payment) | Cash or equivalent paid upfront. |
| Tv (Trade-in Value) | Amount credited by dealer for your trade-in. |
| Tb (Trade-in Balance) | Loan payoff still owed on the trade-in. |
| L (Financed) | Loan principal after all adjustments. |
| APR | Annual Percentage Rate of the loan. |
| i | Periodic (monthly) interest rate = APR/12. |
| n | Number of monthly payments (term). |
How it works: a step-by-step example
Example inputs
- Price = $12,000; Down = $1,000; Trade-in value = $1,500; Trade-in balance owed = $2,200
- Sales tax = 8.5%; Fees = $400; APR = 7.49%; Term = 60 months
Compute OTD and financed
OTD = (12,000 − 1,500) × (1 + 0.085) + 400 = 11,025 × 1.085 + 400 = 11,956. ≈ $11,956.
Financed = max(11,956 − 1,000 + 2,200, 0) = $13,156.
Payment
i = 0.0749 / 12 ≈ 0.0062417; n = 60. Payment = iL / (1 − (1+i)^−n) ≈ $264.66.
Total interest ≈ 60×264.66 − 13,156 = $2,723. Total cost ≈ OTD + TI ≈ $14,679.
Frequently asked questions
Do I pay sales tax on the full price or price minus trade-in?
Many jurisdictions tax the net price after trade-in, but rules vary. This calculator assumes tax on (price − trade-in). Adjust your numbers if local rules differ.
How do you handle negative equity?
If loan balance owed on the trade-in exceeds its value, the difference is added back to the amount financed (negative equity is rolled into the new loan).
Is the payment formula the same as a car loan?
Yes—standard amortization. Only inputs (price, fees, taxes) differ.
Can I include extended warranty or accessories?
Add them into the Fees field if they are financed; otherwise include them in your down payment if paid in cash.
What APR and term are typical for motorcycles?
APR and term vary by lender, credit profile, and bike age. Try 36–72 months and compare offers; check lender disclosures for exact terms.
Will making extra payments reduce interest?
Yes. Prepaying principal shortens the term and reduces total interest. Ask your lender about prepayment policies.
How accurate is the payoff date?
It assumes on-time monthly payments starting in the selected month. Actual dates depend on lender posting and your contract’s first-payment date.
Formula (LaTeX) + variables + units
Amount financed: $\\text{OTD} = (P - T_v) \\times (1 + t) + F$ $\\text{Financed} = \\max\\{\\text{OTD} - D + T_b,\\ 0\\}$ where $P$ = price, $T_v$ = trade-in value, $t$ = tax rate (decimal), $F$ = fees, $D$ = down payment, $T_b$ = trade-in loan balance owed (negative equity). Payment (standard amortized loan, monthly): $i = \\dfrac{\\text{APR}}{12}$, $n = \\text{term months}$, $L = \\text{Financed}$ $\\displaystyle \\text{Payment} = \\frac{iL}{1 - (1 + i)^{-n}}$ Total interest: $\\text{TI} = n\\times\\text{Payment} - L$; Total cost: $\\text{OTD} + \\text{TI}$.
- P = principal (loan amount) (currency)
- r = periodic interest rate (annual rate ÷ payments per year) (1)
- n = total number of payments (years × payments per year) (count)
- M = periodic payment for principal + interest (currency)
- T = property tax (annual or monthly depending on input) (currency)
- consumerfinance.gov — consumerfinance.gov · Accessed 2026-01-19
https://www.consumerfinance.gov/ - federalreserve.gov — federalreserve.gov · Accessed 2026-01-19
https://www.federalreserve.gov/ - Home — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/ - Finance — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/finance - Loans & Debt — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/subcategories/finance-loans-debt - Loan Amortization Schedule — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/loan-amortization - Loan Prepayment Planner — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/loan-prepayment - APR Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/apr
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.