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2A-1 In Chapter 2 we dealt only with situations where 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 appendix, we discuss present value and future value calculations when the interest rate is compounded continuously. Continuous Compounding The relationship between discrete and continuous compounding is illustrated in Figure 2A-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 show, the more frequent the compound- ing period, the larger the final compounded amount because interest is earned on interest more often. Equation 2-1 in the chapter can be applied to any number of compounding periods per year as follows. (2A-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 compound- ing periods per year, we obtain the following future values at the end of five years.
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