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this is my first lease also. Leasing means your renting and basically paying for the amount of car that you use. So the term and mileage gets calculated into your payments. However, the amount you use is based on the selling price and als the residual value, about 60% ( and this change every month). So you want a low selling price and a high residual value for a lease, making the difference that you use the car a lower number. Still with me?
Then the other part of the equation comes from the interest that you pay for financing - the rate is the money factor (MF). Which is some mumbo jumbo car dealer number. There is a way to get an actual interest rate from the MF and convert back to normal rates -check out Edmunds.com lease calculator.
Then adding the amount that you use and the interest should be about the monthyl payment.
Of course there is still the down payment. Try not to put anything down on the down payment as you lose this amount if you crash the car and it is totalled. So if you put $3000 down and total it the next day, you just lost $3000