Authoritative Data Source & Methodology

AuthoritativeDataSource: Standard amortization mathematics per finance textbooks and regulator guidance on APR and installment credit (e.g., U.S. CFPB resources for installment loans and the Federal Reserve’s explanations of loan APR and payment computations). Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

We compute the amount financed \(PV\) from purchase inputs, then apply the annuity formula with optional end-of-term residual/balloon \(B\). Let \(i\) be the rate per period and \(n\) the number of periods.

Amount financed: \[ PV = \underbrace{\big(\text{Price} - \text{Down} - \text{TradeIn}\big)}_{\text{Taxable Base}} \;+\; \begin{cases} \text{Tax} & \text{if financed}\\ 0 & \text{if paid up front} \end{cases} \;+\; \begin{cases} \text{Fees} & \text{if financed}\\ 0 & \text{if paid up front} \end{cases} \]

Per-period rate: \(\; i = \dfrac{\text{APR}}{\text{periods per year}}\)

Payment with balloon \(B\) due at maturity: \[ \text{Payment} = \frac{\big(PV - \frac{B}{(1+i)^n}\big)\, i}{1 - (1+i)^{-n}} \] For \(B=0\) this reduces to the standard annuity: \[ \text{Payment} = PV \cdot \frac{i}{1-(1+i)^{-n}} \]

Interest each period: \(\text{Interest}_t = \text{Balance}_{t-1}\cdot i\), Principal: \(\text{Principal}_t = \text{Payment} - \text{Interest}_t\).

Glossary of Variables

  • Equipment Price: Gross price before down payment or trade-in.
  • Down Payment: Cash paid up front to reduce financing.
  • Trade-in Value: Credit for existing equipment; often reduces taxable base.
  • Sales Tax Rate: Jurisdictional tax applied to the taxable base; can be financed or paid up front.
  • Fees: Title, documentation, delivery, or other charges; can be financed or paid up front.
  • APR: Nominal annual percentage rate; converted to rate per period by payment frequency.
  • Term: Loan length in months or years.
  • Payment Frequency: Monthly (12/yr), quarterly (4/yr), or annual (1/yr).
  • Residual/Balloon: Lump sum due at maturity that lowers periodic payments.

How It Works: A Step-by-Step Example

Scenario: Price \$50,000; down \$5,000; trade-in \$0; tax 8.5% (financed); fees \$300 (financed); APR 7.25%; term 60 months; monthly payments; balloon \$10,000.

  1. Taxable base = \$50,000 − \$5,000 − \$0 = \$45,000; tax = \$45,000 × 8.5% = \$3,825.
  2. Financed PV = \$45,000 + \$3,825 + \$300 = \$49,125.
  3. Monthly rate \(i = 0.0725 / 12 = 0.0060417\); \(n=60\); balloon \(B=\$10{,}000\).
  4. Payment \(= \big(PV - \frac{B}{(1+i)^n}\big)\frac{i}{1-(1+i)^{-n}}\).
  5. Schedule shows each period’s interest and principal; final period leaves \$10,000 balloon due.

Frequently Asked Questions

How do trade-ins affect sales tax?

In many jurisdictions, trade-in reduces the taxable base (price − trade-in). Some areas tax full price. Confirm local rules.

Balloon vs. residual—are they the same?

Both are end-of-term lump sums. “Residual” is common in leases; “balloon” in loans. This tool supports a balloon for loans.

Can I compare monthly vs. quarterly payments?

Yes—switch frequency. The APR is converted to a per-period rate, so payment size changes with the number of periods per year.

Does the calculator include depreciation or tax deductions?

No. Use this for payment mechanics. Consult your accountant about Section 179, bonus depreciation, and interest expensing.

Why is my lender’s payment slightly different?

Day count conventions, compounding cutoffs, fees, and exact tax rules vary. Use this as a high-fidelity estimate.

Tool developed by Ugo Candido. Content verified by the CalcDomain Editorial Board.
Last accuracy review: