Geoscience Reference
In-Depth Information
n
AP
i
(
+
+−
1
i
)
=
(10.1)
n
(
1
i
)
1
where
A
= Annual investment or payment ($).
P
= Present value ($).
i
= Interest rate (%).
n
= Number of years.
■
EXAMPLE 10.1
Problem:
How much will an investment of $5000 yield annually over 8 years at an interest rate of 5%?
Solution:
8
=
0051 005
1005
.(
+
.)
A
=
$
5000
0 154
.
7
8
(
+
.
)
−
1
=
$
5000 0 1547
( .
)
=
$.
773 50
$5000 invested at 5% for 8 years will yield an annual payment of $773.50.
Note:
The higher the interest rate (
i
) earned by the investment, the higher the annual amount will
be, because annual amounts compound at a higher rate. On the other hand, the longer the
term of the investment (
n
), the lower the annual amount will be, because there are more
annual payments being made that compound for a longer time.
10.3 UNIFORM SERIES PRESENT WORTH (VALUE) FACTOR
The present worth of an amount of money is the equivalent of either a single amount in the future
(the future amount) of a series of amounts to be received or paid annually over a period of years as
compounded at an interest rate over a period of years. Stated differently, what must the investment
be now so a future series of money can be received? The present worth can be calculated from a
single future amount (
F
) or an annual amount (
A
). Here, the present worth (
P
) of a series of equal
annual amounts (
A
) can be calculated by using Equation 10.2, which compounds the interest (%) at
which the annual amounts are invested over the term of the investment in years (
n
):
n
(
1
+−
+
i
)
1
PA
=
(10.2)
n
i
(
1
i
)
■
EXAMPLE 10.2
Problem:
The present worth of a series of eight equal annual payments of $154.72 at an interest rate
of 5% compounded annually will be what?
Solution:
8
(
1005
+
.
)
−
1
P
=
$.
154 70
8
0051
.(
+
005
.)
=
$
15
447264632
.(.
)
=
$
1000
Search WWH ::
Custom Search