How to Calculate the Effective Interest Rate for Leases

Many consumers who choose to lease a vehicle aren't aware that they're effectively paying interest in addition to the amount the vehicle depreciates over the lease term. Automotive dealers aren't required to disclose the effective interest rate in their lease contracts. Financing charges are usually referred to as a "money factor," a decimal figure with little obvious correlation to typical interest rate yields, and aren't usually disclosed to customers. With the application of Newton's method and basic financing formulas, a lessee can determine the effective interest rate he pays on a vehicle lease.

Instructions

1

Determine the depreciated amount of the vehicle over the course of the lease term by subtracting its sticker price from its declared value at the end of the lease. Let this value be variable A. For example, a $20,000 car that is worth $12,000 at the end of its lease has a final value of $8,000, so A = 8000.

2

Set variable P as the monthly payment amount, and variable N as the total number of monthly payments in your lease term. In the example, the lessee agrees to pay $164.21 monthly on a five-year lease -- 60 total monthly payments -- so P = 164.21 and N = 60.

3

Research common automotive loan rates for your area, and reduce that figure to a monthly interest rate by dividing it by 12 set that variable to I. Newton's method relies on trial and error to reach its final calculation, so starting with an estimate of a likely interest rate should help streamline your calculations. In the example, above, interest rates in the area are 8 percent, which is equivalent to 0.0067 interest monthly. So I = 0.0067.

4

Apply the variables to the monthly payment formula to determine if your estimate was accurate.

Pp = I * 8,000/[1 -- (1+I)^-n]

So, for our example:

Pp = 0.0067 * 8000/[1 -- (1+0.0067)^-60]

Pp = 162.37

If Pp = P, the estimate used to determine the interest rate, I, was accurate. The interest on the loan is I multiplied by 12. If not, continue to Step 5

5

Apply Newton's method to find a new test value for I, known a Ix, using the Pp value determined in the previous step.

Ix = I -- ([Pp-Pp*(1+I)^-N --I*A]/[N*Pp*(1+I)^-(n -- 1) -- A)

For the example,

Ix = 0.0067 -- ([162.37-162.37*(1+0.0067)^-60 -- 0.0067* 8,000]/60 * 162.37 *(1+0.0067)^ -- (60 -- 1) -- 8,000)

Ix = 0.0069

6

Set I = Ix, and return to Step 4. After a few permutations of Newton's method, we arrive at I = 0.0071 for our example, which results in a Pp value of 164.21, the same value as P. The interest rate on the lease was 8.5 percent.