Geoscience Reference
In-Depth Information
■
EXAMPLE 10.4
Problem:
A man read that in the western United States a 10-acre parcel of land could be purchased
for $1000 cash. The man decided to save a uniform amount at the end of each month so that he
would have the required $1000 at the end of one year. The local bank pays 1/2% (0.005) interest,
compounded monthly. How much would the man have to deposit each month?
Solution:
Given that
F
= $1000,
if
= 0.05, and
n
= 12,
if
AF
=
n
(
1
+−
if
)
1
0 005
10005
.
=
$
1000
12
(
+
.
)
−
1
=
$
1000 0 0811
( .
)
=
$.
81 10
The man would have to deposit $81.10 each month.
Note:
The higher the interest rate (
if
) earned by the investment, the lower the annual amount will be,
because the annual amounts can compound at a lower rate to reach the same future amount.
The longer the term of the investment (
n
), the higher the annual amount will be, because
there are more annual payments being made that compound for a longer time.
10.6 PRESENT VALUE OF FUTURE DOLLAR AMOUNT
The present value of an amount of money is the equivalent of either a single amount in the future
(the future amount) or a period of years as compounded at an interest rate over a period of years.
The present value can be calculated from a single amount (
F
) or an annual amount (
A
). The pres-
ent value (
P
) of a future dollar amount (
F
) can be calculated by using Equation 10.5. The equation
compounds the interest in percent (
if
) at which the present value (
P
) is invested over the term of the
investment in years (
n
).
=+
−
n
PF if
(
1
)
(10.5)
■
EXAMPLE 10.5
Problem:
What is the present value of $6000 to be received in 5 years if it is invested at 6%?
Solution:
−
n
PF if
=+
(
1
)
5
1
006
−
5
=
$
6000 1006
(
+
.)
=
$
6000
.
=
$
6000 0 747
( .
)
=
$
4482
The present value of $6000 to be received in 5 years, if it is invested at 6%, is $4482.
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