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78106_04_Web_Ch04C_p01-03 - WEB EXTENSION 4C Continuous...

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W E B E X T E N S I O N 4C Continuous Compounding In Chapter 4 we dealt only with situations in which interest is added at discrete intervals annually, semiannually, monthly, and so forth. In some instances, though, it is possible to have instantaneous, or continuous, growth. In this extension we discuss present value and future value calculations when the interest rate is compounded continuously. 4.1 C ONTINUOUS C OMPOUNDING The relationship between discrete and continuous compounding is illustrated in Figure 4C-1. Panel a shows the annual compounding case, where interest is added once a year; Panel b shows the situation when compounding occurs twice a year; and Panel c shows interest being earned continuously. As the graphs illus- trate, the more frequent the compounding period, the larger the final com- pounded amount because interest is earned on interest more often. Equation 4-14 in the chapter can be applied to any number of compounding per- iods per year: More frequent compounding : FV N ¼ PV 1 þ I NOM M ± ² MN (4C-1) Here I NOM is the stated annual rate, M is the number of periods per year, and N is the number of years. To illustrate, let PV = $100, I = 10%, and N = 5. At various
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