Show that, as the time interval of compounding goes to zero, the bank balance after k years

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Show that, as the time interval of compounding goes to zero, the bank balance after k years approaches an exponential function erk a, where r is the yearly interest rate and a the initial balance.
Compounding
Compounding is the process in which an asset's earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will...
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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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