# Compound interest, Napier's constant and concept of limit

The problem is: "If we invest 1 € at a compound interest rate of 100% per year after one year the accumulated capital is 2 €. What is accumulated capital worth after one year if, instead of using the annual rate of 100%, we use a semi-annual rate of 50% or a quarterly rate of 25%? Proceeding thus, with the help of the GeoGebra spreadsheet, with a monthly rate and then daily, hourly, per minute, what do we notice? ". The construction shows how this problem is solved with a graphical representation in GeoGebra in which the variable on the y-axis represents successive approximations of Napier’s constant. There is both a recursive solution, fractioning the annual period and a solution based on the computation of the nth term of the sequence. The y-axis plots values that may be overlapping: these can be separated visually using GeoGebra’s zoom tool. The graph clearly shows the intuitive conclusion that the limit is a number, from a dynamic viewpoint, it is the outcome of a process and not the process itself as students often think.

Material Type
Worksheet
Tags
interest  napier  constant  limit
Target Group (Age)
15 – 18
Language
English (United Kingdom)

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