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Effective Lease Rate Calculator (Hidden APR Finder)

Calculate the true Effective Interest Rate (APR) in a car lease. Reverse-engineer the hidden rate from Cap Cost, Residual, and Monthly Payment using Newton-Raphson iteration.

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Category Car Calculators
Negotiated Price - Down Payment
Value at end of lease
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About

Automotive lease agreements often obfuscate the actual cost of borrowing by using opaque terms like "Money Factor" or "Rent Charge." While dealerships focus on the monthly payment, the embedded interest rate is a critical determinant of the deal's value. The "Money Factor" approximation (APR ≈ MF × 2400) is merely a heuristic; it does not account for the timing of payments or complex fee structures.

To determine the true annual percentage rate, one must solve for the internal rate of return that equates the Net Capitalized Cost (the loan amount) with the present value of the residual value plus the stream of annuity payments. Since this equation is non-linear, it cannot be solved with simple algebra. This tool utilizes the Newton-Raphson numerical method to iterate toward the precise interest rate, ensuring transparency in financial decision-making.

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Formulas

The calculator solves for the periodic interest rate r in the following Time Value of Money equation:

Cadj − Vres(1 + r)n = P × 1 − (1 + r)−nr

Where:

  • Cadj: Adjusted Capitalized Cost (Price - Down Payment).
  • Vres: Residual Value (End of Lease).
  • P: Monthly Payment.
  • n: Total number of months.
  • r: Monthly Interest Rate (APR / 12).

Reference Data

Term (Months)Money Factor (MF)Approx. APR (MF × 2400)Credit Tier
24 - 360.000501.2%Super Prime
24 - 360.001253.0%Prime
24 - 360.002506.0%Standard
36 - 480.003338.0%Sub-Prime
Any0.0041610.0%High Risk

Frequently Asked Questions

Money Factor (MF) is a different notation for interest used primarily in leasing. To convert MF to APR, multiply by 2400. For example, an MF of 0.0025 is equivalent to 6% APR. Dealerships often quote MF because the small decimal looks less intimidating than the percentage.
Advertised lease deals often exclude taxes, acquisition fees, and dealer fees from the APR calculation. If these are rolled into your Capitalized Cost but the dealer calculates payment based on the base price, the effective rate you are paying on the total balance is higher.
Yes. If you make no down payment, simply enter the full Negotiated Price as the Gross Capitalized Cost. The calculator determines the cost of financing that entire amount over the lease term.
The Residual Value determines how much of the car's value you are NOT paying for during the lease. A higher residual value typically lowers monthly payments, but it might come with a higher interest rate to compensate the lender.