Expert: Paul Klarreich - 4/5/2007

Question
Is there a simpler way to figure out the answer to 1.06^300 than multiplying 1.06 by itself 300 times?  If so could you please explain how?  I haven't done this in years and am trying to help child with homework.

Answer
Hi, Denise,

Your question:
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Is there a simpler way to figure out the answer to 1.06^300 than multiplying 1.06 by itself 300 times?  If so could you please explain how?  I haven't done this in years and am trying to help child with homework.
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depends on the level your child has reached.  [OK, OK, you didn't say it was YOUR child.]

The technique might involve the concept of logarithms, in which you do something like this:

X = 1.06^300

log X = 300 log 1.06

Now you can determine  log 1.06 by a printed table or by your scientific calculator (you can use the one in Windows, setting the view to scientific).

Then you multiply the result by 300, getting something around  7.6.

Finally you do the INVERSE LOGARITHM. (Click Inv, then LOG)

The answer on mine is 39062459.05

But this is not necessarily the easiest way.  In fact, you can just do this sequence on the Windows calculator:

Clear
Enter 1.06
Press x^y
Enter 300
Press =

and get the same answer.  No doubt the calculator does the same steps I outlined earlier, but hidden from your view.