Let's begin by coming up with a simple mathematical model of annual
interest. Suppose that you invest P dollars in a bank account that
pays annual interest at a rate of R. This means that at the
beginning of the first year you have P dollars. After one year, the
bank gives you an additional PR dollars, giving you a new balance of
P + PR dollars. One year later your balance again increases by a
factor of R, giving you
dollars. A year after this, you have
dollars. Can you generalize this process to determine how much money you'll
have after n years?
Spotting the pattern in these increasingly longer formulas isn't necessarily
easy. Let's see if Maple can help. Maple has a built-in function called
factor that will factor a complex expression. Let's factor the expressions
that give the amount of money after:
A pattern that suggests a formula for the amount of money in the
account after n years begins to emerge. What is it? Can you
explain why it makes sense?
Click here for the answer
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah