The Economic Consequences of Homelessness in The US

This monthly payment formula is easy to derive, and the derivation illustrates how fixedrate
mortgage loans work. The amount owed on the loan at the end of every month
equals the amount owed from the previous month, plus the interest on this amount,
minus the fixed amount paid every month.
Amount owed at month 0:
Amount owed at month 1:
( principal + interest – payment)
(equation 1)
Amount owed at month 2:
Using equation 1 for
Amount owed at month 3:
(equation 2)
Using equation 2 for
Amount owed at month N:
Where
progression)
(equation 3)
(equation 4) (see geometric
(equation 5)
With the exception of two terms the and series are the same so when
you subtract all but two terms cancel:
Using equation 4 and 5
(equation 6)
Putting equation 6 back into 3:
will be zero because we have paid the loan off.
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