# Great explanation of the math behind the moneyfactor

I recently found this article and think it is the best way to explain the math behind the moneyfactor.

http://www.alphaleasing.com/Resources/Articles/MoneyFactor.asp

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Thanks for the article. I understand very clearly how to calculate the payments, but I still am confused as to why the formula is the way it is. Below are 2 sections that Iâ€™m still confused about. Maybe can you help further explain?

Interest Calculation: The average balance for a loan that you are incrementally paying down to zero will always be the original amount divided by 2. So the average balance in this case is \$7,500 (\$15,000/2). Monthly interest on \$7,500 is \$37.50.

I donâ€™t understand how this is calculating interest. Where/what is the interest rate used in that calculation?

Interest Amount: (Adjusted Capital Cost + Residual) * Money Factor Interest Amount: (\$25,000 + \$10,000) * .0025 = \$87.50

This is the main forumula to calculate the interest amount. Why is it adj cap cost + RV? If the vehicle is \$25k, why do I pay interest on \$35k? I would think that Iâ€™d only pay interest on \$25k.

Why is it adj cap cost + RV? Because youâ€™re paying interest on the average of the two, i.e. (Adj Cap cost + RV)/2

Youâ€™re not paying interest on 35k, youâ€™re paying interest on 17.5k

Ahh, that makes sense now. So the formula is actually more like: (cap cost + RV)/2 * (interest/12). Thatâ€™s why you multiple/divide by 2400 to convert between interest/MF. Thanks.

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Exactlyâ€¦

â€¦20 char

Money factor is NOT an average of cap cost plus residual. There is NO divided by 2 in the lease interest calculation.

It is literally Adjusted Cap Cost plus Residual times the decimal money factor. The higher the cap cost and the residual of a car the much more interest you will pay even if the money factors are the same.

Lease interest is compounded the higher the price and residual are. Basically donâ€™t lease a very expensive car with a high interest rate. The interest will become very burdensome.

Read a couple posts below that. INTEREST is charged on the average of cap cost + residual value.

Yes there is. Itâ€™s part of the 2400x factor that converts from interest rate to money factor.

MF=Annual Interest rate percentage * 1/100 (converts percent to decimal) * 1/12 (converts annual to monthly) * 1/2 (the 2 for the average)

1/100 * 1/12 * 1/2 = 1/2400

MF = Annual interest rate percentage * 1/2400

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Exactly as @mllcb42 described above: the same way the RV is an estimation, the MF is also an estimation. They hedge the risk by taking the average of the cap cost and the RV, hence (Cap Cost + RV) / 2.

The Calculation for converting money factor to an interest rate is an approximation. The calculation for actual interest paid each month on a lease is NOT an approximation.

For example if you calculate interest on a lease with a 50% residual and then compare it to the exact same lease with a 53% residual you will see that the higher residual actually pays slightly more interest each month even with the exact same decimal money factor.

If you went from 15k Miles a year to 10k Miles per year you would typically see a 3% higher residual and the money factor is often still the exact same. In that case you will actually pay slightly more interest on the lower mileage lease even though both your money factor AND your approximate equivalent interest rate would be the same.

You all are making the mistake of trying to convert lease interest into an equivalent loan interest rate. There is no direct conversion that is always accurate. It will always be an approximation.

I will say it again. When calculating the actual interest you pay each month on a lease it varies with the sum of the adjusted cap cost AND the residual and there is no â€śaverageâ€ť of those values in that calculation.