Environmental Engineering Reference
In-Depth Information
in the initial year, the capital
c
n
after a time of n years, with the interest rate
ir
,
can be estimated using compound interest formulae. With
q
= 1 +
ir
,
(6.4)
the expression becomes:
c
n
=
A
0
•
(1 +
ir
)
n
=
A
0
•
q
n
(6.5)
For an initial capital of
A
0
=
6500 (following the example of the photovoltaic
system in the section headed 'Costs for a photovoltaic system', p237) invested
with an interest rate of
ir
= 6 per cent = 0.06 over a time of
n
= 25 years,
the capital after 25 years including interest becomes
€
6500
•
(1 + 0.06)
25
=
c
25
=
27,897
€
€
Later payments yield interest as well, though over a lower term. If the investor
pays another
1500 after 10 years (for a replacement inverter), the term
reduces to 15 years. The capital after 25 years would then be:
€
=
A
0
·
q
25
+
A
10
·
q
15
=
6500 · 1.06
25
+
1500 · 1.06
15
=
c
25
€
€
€
31,492
The following formula describes this in general:
(6.6)
If all payments
A
i
in the different years
i
are the same, the geometric
progression provides the following formula:
(6.7)
For later payments it is necessary to calculate the additional capital that would
have to be invested at the beginning with the interest rate
ir
so that the capital
at the end of the investment period is the same.
The payment
A
i
in the year
i
can be discounted to the initial year:
(6.8)
Thus, the respective initial capital for a payment of
1500 after 10 years for
€
the example above becomes:
A
10/0
=
1500 · 1.06
-10
=
838
€
€
