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Unformatted text preview: 1 X 10% = $0.10) and adding the $0.10 to
the original dollar. And, if the resulting $1.10 is invested for another year at 10%, how much will
you have? The answer is $1.21. That is, $1.10 X 110%. This process will continue, year after year. The annual interest each year is larger than the year before because of “compounding.”
Compounding simply means that your investment is growing with accumulated interest, and you are
earning interest on previously accrued interest that becomes part of your total investment pool. This
formula expresses the basic mathematics of compound interest:
(1+i) n Where “i” is the interest rate per period and “n” is the number of periods
So, how much would $1 grow to in 25 years at 10% interest? The answer can be determined by
taking 1.10 to the 25th power [(1.10)25], and the answer is $10.83. Future value tables provide
predetermined values for a variety of such computations (such a table is found at the FUTURE Download free ebooks at bookboon.com
22 Compound Interest and Present Value Analytics for Managerial Decision Making VALUE OF $1 link on the companion website). To experiment with the future value table,
determine how much $1 would grow to in 10 periods at 5% per period. The answer to this question
is $1.63, and can be found by reference to the value in the “5% column/10-period row.” If the
original investment was $5,000 (instead of $1), the investment would grow to $8,144.45 ($5,000 X
1.62889). In using the tables, be sure to note that the interest rate is the rate per period. The “period”
might be years, quarters, months, etc. It all depends on how frequently interest is to be compounded.
For instance, a 12% annual interest rate, with monthly compounding for two years, would require
you to refer to the 1% column (12% annual rate equates to a monthly rate of 1%) and 24-period row
(two years equates to 24 months). If the same investment involved annual compounding, then you
would refer to the 12% column and 2-period row. The frequency of compounding makes a
difference in the amount accumulate...
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