Agriculture Reference
In-Depth Information
For example, if someone saved $1,000 each year for the next 25 years and invested that
amount at 6 percent and the interest earned each year remained invested the amount at the
end of 25 years would be:
Future Value
(
54 864
)
$1
=
000
864.
$,
54
=
The factor, 54.864, is the factor for 25 years and 6 percent. Also, if an individual wanted to
accumulate $1,000,000 over a 25-year career in order to retire and the interest rate was
assumed to be 5 percent, the amount could be calculated as shown below:
(
)
$,
,
A
mount Needed to Invest Each Year
47 726
,
,
.
000
Amount Needed to Invest Each Year
$,
,
9
5
=
.
The factor, 47.726 was taken form Table 13.3 and is the factor for 25 years and
5 percent.
Of course, one approach to determine the present value of the entire stream is to
fi nd the present value of the income or cost each year and then sum the present values
for each of the years. Alternatively, in situations in which there are equal periodic
amounts with a constant discount factor the computational procedure can be simplifi ed
by using discount factors for an annuity. Again, there are situations in which a future
series of cash payments would need to be discounted to the present value. This includes a
series of equal loan payments over a repayment schedule or to determine the value of a
series of payments that will be paid from an annuity that is being considered for
retirement. Discount factors for selected interest rates and periods are provided in
Table 13.4 .
For example, if an individual borrowed $100,000 to purchase a house and the repayment
period was 25 years and the interest was 5 percent, the amount of the annual payment could
be calculated as follows:
nnual Payment 14
(
)
$,
,
A
0
939
.
000
5. 7Annual Payment
$,
,
9
Again, the factor, 14.0939, was taken from Table 13.4 and is the discount factor for a uni-
form series of 25 years and for 5 percent.
Non-annual periods
Non-annual periods can also occur when compounding and discounting and should also
be discussed. Up until now, all of the compounding and discounting examples have involved
annual periods. However, institutions can compound quarterly, monthly, and even daily. Likewise,
many payments are scheduled to be due monthly rather than annually. Fortunately, the
compounding for a period shorter than a year can be handled the same as for annual compound-
ing and discounting, except the period and the interest rate must match. For example, if a person
invests money for fi ve years with quarterly compounding at a 4 percent annual rate, the number
of periods increases from fi ve years to 20 quarters. Likewise, the rate is no longer 4 percent per
 
 
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