Lesson 19 of 25 · 6 min

Lease payment arithmetic

The monthly figure is two charges stacked: one for the scheduled fall in the mark, and one for the use of money.

The lease payment splits into two charges with two causes. Depreciation is the scheduled fall, capitalized cost minus residual, spread across n months. Rent is the money factor applied to the sum of those two marks. Track 1 lesson 13 splits a rate into index plus spread: two parts, two causes. This lesson is that split on a lease.

Same book as lesson 18. Thirty-six payments of $501.97 total $18,070.92. The residual of $16,848 is never paid unless the lease is closed by buying the car. Adding $18,070.92 to $16,848 produces $34,918.92, which is not a loan total and not a cash price. It is 36 months of path plus the future mark the contract named. Only the $18,070.92 is the lease's cash claim if the car is returned on the residual's terms.

The two parts of each $501.97 stay in proportion as the months pass, because a standard closed-end lease does not re-amortize. $398.67 is always the fall. $103.30 is always the rent. A loan installment from lesson 10 does the opposite: the interest slice shrinks as the balance shrinks. That is why comparing $501.97 with $560.74 from lesson 2 compares two different machines.

Lesson 20 is what happens when the mark at month 36 is not $16,848. This one is only the addition. Two causes, one monthly figure, a residual that is not in the $18,070.92.

The residual is not hidden inside the payment. It sits outside the $18,070.92, as a future mark the contract already named.

Key terms

Depreciation charge: Capitalized cost minus residual, divided by n. The scheduled fall, in monthly cash.
Rent charge: Money factor times (capitalized cost plus residual). The use-of-money slice of the payment.
Lease cash claim: The payments over the term. It does not include the residual unless the lease is closed by buying the car.

Worked example

Thirty-six months, residual not included

Same Marlow Street Garage book as lesson 18. Payment $501.97. Residual $16,848.

Thirty-six payments: $18,070.92
Of each payment, depreciation: $398.67
Of each payment, rent: $103.30
Residual: $16,848
Payments plus residual: $34,918.92

The lease's cash claim, if the car is returned on the residual's terms, is $18,070.92. The $16,848 is a future mark, not a thirty-sixth-and-a-half payment.

Check yourself

Capitalized cost $22,400, residual $12,880, money factor 0.00190, 24 months. What is the depreciation charge, the rent charge, and the payment? What do 24 payments total, and is the residual in that total?

The lease payment splits depreciation from rent the way Track 1 lesson 13 splits a rate into index plus spread: two parts, two causes. Open Variable rates: how index plus spread works →

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.