One of the most familiar economic models is the fixed interest rate model. In
its various forms, it can be used to understand such phenomena as the annual
growth of an investment, the effects of inflation, the result of unchecked
population growth, and the spread of infectious diseases.
Here is the compound interest problem in its simplest form. Suppose that you
invest P dollars in a bank account that pays annual interest at a rate R.
(For example, 5% interest would be an interest rate of .05.) The interest is
credited to your account at the end of each year, at which point you begin
earning interest on the interest. How much money will you have in your account
after n years? Try to come up with a formula, involving P, R, and n,
that gives the answer.
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At the beginning (year 0) you have P dollars. After one year, you'll still
have the P dollars, plus P*R more, for a total of P*(1+R). By the same
reasoning, after two years you'll have P*(1+R)*(1+R), Generalizing, at the
end of n years you'll have P*(1+R)^n dollars. Notice that this formula
works even for n = 0, when it reduces to simply P.
Let's enter the formula into Mathematica so that you can see it printed out in an
easier-to-read form:
P*(1+R)^n
The formula is now sitting in the Mathematica window, but it isn't very useful for
computational purposes. What would you have to do to figure out what $100
invested at a rate of .05 would be worth after 50 years?
Click here for the answer
You'd have to reenter the formula, only this time using 100 instead of P, .05
instead of R, and 50 instead of n. Try it out for a few different numbers.
Because the formula's pretty short, this isn't too much of a pain to do. But a
more complicated formulaÐor even this one, if you try to use it
tomorrowÐmight be difficult to remember. It would be handy if you could
calculate compound interest by entering something like Compound[P,R,n].
Unfortunately, Mathematica has no built-in compound interest calculation function.