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In some loan situations, especially car leases, people like to talk about the money factor, which is a number given by

interest percentage/2400

Where does the 2400 come from? I understand that it is the universal number to use, however I would like to know why that number?

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  • A relevant link. One could probably go through everything they're doing in that link and convert it into algebra.
    – Micah
    Commented Nov 19, 2014 at 18:32
  • Note that when you google "money factor", you get a lot of pages defining it as "interest rate divided by 2400" (that is, this is a genuine piece of terminology, which always means what the OP wants it to mean) and pretty much no page that actually says why -- you can reverse engineer it from the link I left, but it takes a bit of work. This may be more on-topic in Money.SE than it is here, but I think it's a perfectly reasonable question.
    – Micah
    Commented Nov 19, 2014 at 20:04
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    I think it is a reasonable question. The quick answer is that it comes from $2400=2 \cdot 12 \cdot 100$ The $100$ is converting percentage to decimals, the $12$ is converting yearly interest o monthly interest, and the $2$ is to get the average principal balance over the loan. You are multiplying the sum of the starting value and the ending value by this, so dividing by $2$ gets you the average, which you then charge interest on.
    – Ross Millikan
    Commented Nov 19, 2014 at 20:25

4 Answers 4

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A lease payment is composed of an interest portion (borrowed money) and depreciation amount (purchase - residual).

The Monthly payment is then Monthly Interest Cost + Monthly Depreciation Cost

The Money Factor is used to estimate the amount of interest due in a single month of a lease so you can figure out the monthly payment.

If you are borrowing $100,000 then over the entire loan of repayment from a balance of $100,000 to a balance of $0, the average amount you owed was $50,000 (1/2 of principal).

You are repaying this loan monthly (1/12 of a year) and percents are expressed as decimals (1/100).

6 * 1/2 (for principal) * 1/12 (for monthly) * 1/100 (to convert percentage from 6% to .06) = 6 * 1/2400.

2400 is the product of 3 consecutive conversion (1/2 * 1/12 * 1/100) to convert from an interest rate to a money factor.

6/2400 = Money factor of 0.0025 which can be multiplied against the total amount being borrowed to know what the monthly interest would roughly equal.

Some Money Factor info: https://www.alphaleasing.com/resources/articles/MoneyFactor.asp

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    The quote "to know what the monthly interest would roughly equal" is a little vague. Important to say "monthly interest" here is "the percentage of the full loan amount for the average monthly interest payment", and isn't the "monthly interest rate". Money factor X total loan amount = avg monthly interest payment. That's much different than (well, half of) the actual interest rate. 0.0025 * 12 is 3, not 6, eg. You have why - money factor computes the average monthly rate over the life of the loan, and interest drops as principle is paid - but it's a tricky distinction.
    – ruffin
    Commented Jul 22, 2018 at 13:25
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Alex's answer is very helpful. However, I would like to add why it might be convenient to use money factor instead of APR when computing lease payments. Money factor makes it easier to compute the lease payments manually.

Lease payments have two parts:

  1. Depreciation Part
  2. Interest Part

Here is how to calculate them:

  • Depreciation Part = (Capital Cost - Residual Value) / Lease Term
  • Interest Part = (Capital Cost + Residual Value) * Money Factor
  • Monthly payment = Depreciation Part + Interest Part

Where,

  • Capital Cost is the (negotiated) cost of the vehicle, subtracted by any down payment.
  • Residual Value is the value of the vehicle at the end of the lease.
  • Lease Term in months.

This is a computation that anyone can perform without any tools.

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I finally understood the concept of money factor. To me, two things were key:

  1. The APR and finance charge is on the value of the ENTIRE car (not the depreciation). Due to the fact that many people define lease as buying the deprecation, I was for a long time under the impression the interest is only on the depreciated amount.

  2. The straight line depreciation (or linear deprecation) is a key concept. When you understand it, you will understand that the average value of the ENTIRE car is equal to (Cap Cost + Residual Value)/2. The 12 is there only because APR is related to a year and money factor quoted by the car company is used to calculate the monthly fee. The 100 is there only because you want to express the APR as %.

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Let's do it mathematically. Since here it is pretty difficult to use formulas I saved it as an image:

The mathematical steps

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