I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on the different definitions of that appear in Precalculus and Calculus.
Part 1: Justification for the formula for discrete compound interest
Part 2: Pedagogical thoughts on justifying the discrete compound interest formula for students.
Part 3: Application of the discrete compound interest formula as compounding becomes more frequent.
Part 4: Informal definition of based on a limit of the compound interest formula.
Part 5: Justification for the formula for continuous compound interest.
Part 6: A second derivation of the formula for continuous compound interest by solving a differential equation.
Part 7: A formal justification of the formula from Part 4 using the definition of a derivative.
Part 8: A formal justification of the formula from Part 4 using L’Hopital’s Rule.
Part 9: A formal justification of the continuous compound interest formula as a limit of the discrete compound interest formula.
Part 10: A second formal justification of the continuous compound interest formula as a limit of the discrete compound interest formula.
Part 11: Numerical computation of using Riemann sums and the Trapezoid Rule to approximate areas under .
Part 12: Numerical computation of using and also Taylor series.
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