
96 Principles of Sustainable Energy Systems
2.8 Capital Recovery Factor
In many economic analyses, a series of annual or monthly sums is invested or used to pay
off a loan. The series of equal periodic payments necessary to pay off such a loan is deter-
mined as follows. If a sum P
sum
is invested each year at interest rate i, the present worth of
the sum of these payments S is
S
annann ann
=
+
+
+
+
+
+
, (2.15)
or
SP ii
ann
t
=+
()
++
()
++
()
+++
−−
11
123
The expression in the following brackets is a geometric series with the rst term P
ann
/(1 + i)
and ratio (1 + i)
−n
. It follows from the expression for the sum of such a series that ...