Doubling an Investment

If we invest $1000 at 8% interest, compounded annually, how many years will
it be before our investment is worth $2000? Using our definition of
compound, it is not hard to set up an equation for Mathematica to solve that will
give you the answer to this question. The answer is a little over 9, but be
sure that you can make Mathematica give you the answer before continuing.

Now let's generalize the question a bit. If we invest $P at 8% interest,
compounded annually, how many years will it be before our investment is worth
$2*P? You can use virtually the same equation to solve this problem, and
once again the answer is a little over 9. Again, be sure that you can make
Mathematica give you the answer before continuing.

Apparently, the doubling time doesn't depend upon the initial investment, but
it does, of course, depend upon the interest rate.

Let's generalize the problem one step further. If we invest $P at an interest
rate of R, compounded annually, how many years will be it before our investment
is worth $2*P? This is exactly like the last question, except that we must use
an interest rate of R instead of .08.

Not surprisingly, the answer involves R. Now take this answer and turn it
into a function called doubling that will take R as an argument and
return the doubling time for an investment at interest rate R.

Try the function out. Notice that the answers are all given as products
involving the natural log of 2. See if you can doctor the definition of
doubling so that it will always give out a floating point answer.