Louisiana State University



Section 3.1: The Constant e and Continuous Compound InterestTopic 1: The Constant eThe constant number ee=limn→∞1+1nn or, alternatively, e=lims→01+s1sThe number e is irrational and approximately 2.718 281 828 459…The two limits used to define e are unlike any we have encountered so far. Some people reason incorrectly that both limits are 1, since 1+s→1 as s→0 and 1 to any power is 1. Consider the following table of values for s and fs=(1+s)1s and the graph below for s close to 0. Compute the table values with a calculator yourself, and try several values of s even closer to 0. Note that the function is discontinuous at s=0.s-0.5-0.2-0.1-0.01→0←0.010.10.20.5(1+s)1s4.00003.05182.86802.7320→e←2.70482.59372.48832.2500Topic 2: Continuous Compound InterestRecall: The fee paid to use another’s money is called interest. It is usually computed as a percent, called the interest rate, of the principal over a given period of time. The Compound Interest Formula isA=P1+rmmtwhere m,r, and P are constants, t represents time, P represents principal or the initial amount, A represents future value, r represents interest rate, m represents number of times it is compounded per year.The Continuous Compound Interest Formula isA=Pertwhere P and k are constants, t represents time, P represents principal or the initial amount, A represents future value, r represents interest rate. ................
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