Money Factor Background: A Mathematical Proof
Notations |
C: |
The total loan amount. In the case of an auto lease, this is the car price. |
F: |
The residual value. |
r: |
The monthly interest rate. If the annual interest rate is R%, the monthly
interest rate r is R/1200. |
N: |
The term, or the number of months of a lease. |
P: |
The monthly payment. |
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The monthly payment formula for a lease is given by:
When and , one can write:
Using the above expression, the average interest paid per month can be written as:
Since , one can rewrite the average interest payment as:
Hence, the Money Factor can be used to conveniently and reliably
estimate the average interest rate on loans.
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Glossary