Beginning and Intermediate Algebra - Wallace Math Courses ...

The variable e is a constant similar in idea to pi (π) in that it goes on forever
without repeat or pattern, but just as pi (π) naturally occurs in several geometry
applications, so does e appear in many exponential applications, continuous
interest being one of them. If you have a scientific calculator you probably have
an e button (often using the 2nd or shift key, then hit ln) that will be useful in
calculating interest compounded continuously.
World View Note: e first appeared in 1618 in Scottish mathematician’s
Napier’s work on logarithms. However it was Euler in Switzerland who used the
letter e first to represent this value. Some say he used e because his name begins
with E. Others, say it is because exponent starts with e. Others say it is because
Euler’s work already had the letter a in use, so e would be the next value. Whatever
the reason, ever since he used it in 1731, e became the natural base.
Example 548.
If S4000 is invested in an account paying 3% interest compounded continuously,
what is the balance after 7 years?
P = 4000, r = 0.03, t=7 Identify each of the variables
A=4000e 0.03·7 Multiply exponent
A=4000e 0.21 Evaluate e 0.21
A = 4000(1.23367806 ) Multiply
A = 4934.71
S4934.71 Our Solution
Albert Einstein once said that the most powerful force in the universe is compound
interest. Consider the following example, illustrating how powerful compound
interest can be.
Example 549.
If you invest S6.16 in an account paying 12% interest compounded continuously
for 100 years, and that is all you have to leave your children as an inheritance,
what will the final balance be that they will receive?
P = 6.16, r = 0.12, t = 100 Identify each of the variables
A=6.16e 0.12·100 Multiply exponent
A=6.16e 12 Evaluate
A = 6.16(162, 544.79) Multiply
A =1, 002, 569.52
S1, 002, 569.52 Our Solution
In 100 years that one time investment of S6.16 investment grew to over one million
dollars! That’s the power of compound interest!
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