That's how it works. Per Edmunds:
1. Sticker price (MSRP) of the car $23,000
2. Times the residual value percentage x 0.57
3. Equals the residual value = $13,110
4. Negotiated selling price of car $21,000
5. Add in fees + $1,200
6. Add lines 4 and 5 to get gross capitalized cost = $22,200
7. Subtract your down payment and rebates - $2,200
8. This is your adjusted capitalized cost = $20,000
9. Subtract the residual value from adjusted capitalized cost.This is your depreciation amount.
$20,000 - $13,110 = $6,890
10. Divide the depreciation amount by number of months in your lease. This will be your base payment.
$6,890/36 = $191.39
12. Add the adjusted capitalized cost and the residual value. Take the sum and multiply it by money factor. This is your monthly rent charge.
($20,000 + $13,110) x 0.00125 = $41.39
13. Add the rent charge to your base payment to get your pretax lease payment
$191.39 + $41.39 = $232.78
14. Multiply your tax rate by the pretax lease payment to get the total lease payment.
$232.78 x 1.095 = $254.89
My method of calculating is:
1. Cost of car $22,200
2. Down payment and rebates $2,200
3. Capitalized cost $20,000
4. Residual $13,110
5. Depreciation $6,890
6. Interest rate .00125 money factor times 2400 = 3%
7. Payment on depreciation of $6,890, 36 months, at 3% APR = $200.37
8. Interest on residual $13,110 x 3% APR x 3 years = $1,179.90
9. Interest on residual per month $1,179.90 / 36 = 32.78
10. Total monthly payment $200.37 + $32.78 = $233.15
11. Sales tax $233.15 x .095 = $22.15
12. Total monthly payment $233.15 + $22.15 = $255.30
My method comes up 41 cents different than Edmunds (immaterial). This illustrates that you are paying off the loss in value as a loan over the lease period, and in addition are paying interest on the residual.
Here is a link to the Edmunds site:
https://www.edmunds.com/car-leasing/calculate-your-own-lease-payment.html