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Unformatted text preview: have at the end of each period. At the end of 12 months (1 year), with 8%
quarterly compounding, Fred will have $108.24; at the end of 24 months (2
years), he will have $117.16.
Table 4.7 compares values for Fred Moreno’s $100 at the end of years 1
and 2 given annual, semiannual, and quarterly compounding periods at the 8
percent rate. As shown, the more frequently interest is compounded, the greater
the amount of money accumulated. This is true for any interest rate for any
period of time. A General Equation for
Compounding More Frequently Than Annually
The formula for annual compounding (Equation 4.4) can be rewritten for use
when compounding takes place more frequently. If m equals the number of times
per year interest is compounded, the formula for annual compounding can be
FVn PV 1 i
m mn (4.18) If m 1, Equation 4.18 reduces to Equation 4.4. Thus, if interest is compounded annually (once a year), Equation 4.18 will provide the same result as
Equation 4.4. The general use of...
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