Hi all,
Here's a very didactic little problem I posed my 12-year old daughter
to let her understand a key mathematical concept. She readily took her
SHARP PC-1350, computed furiously for a while, and was amazed no end by
the result.
You are to try your hand at it with your favorite HP calc, but first you should take a risk and make a decision on what
would be your choice, without any external (electronic or mechanical) help, based on your own
internal calculations and judgment. Then, take your trusty HP calc and find out (most any HP calc will do,
even the HP-01, but built-in unit conversions would be handy if you're not used to metric units).
The little quiz
-
[This is a purely mathematical, ideal problem so physical laws and limits do not
apply, no tricks or word games here. Also no cents are rounded, ever; all amounts are kept to as many decimal places as necessary]
peculiar proposal to you. You must choose the option you deem will result in the greatest amount of money for you, between these two, namely:
- (a) From the instant you accept this one choice, you're given $1.00, which will be placed in a
bank account at 5% compound interest, to be accrued yearly, i.e:, after 1 year you'll
have $1.05, after two years you'll have a little over $1.10 and so on. At the end of
a specified time period you'll be given the resulting balance from your $1.00 initial
capital, plus accrued interests.or
- (b) From the instant you accept this other choice, a cylinder of solid gold, with a
diameter equal to that of the Earth, will start to grow in length at the speed of
light (i.e.: the cylinder's top will reach to the Moon in just over 1 second, to the Sun in 8 minutes, to Sirius in under 9 years, and to Betelgeuse in some 1,400 years). At the end of the specified time period, you'll be given the monetary value corresponding to the cylinder's resulting mass of gold.
Now, taking the diameter of the Earth as 12,700 Km, the speed of light as 300,000 Km per second,
the density of gold as 19 grams per cubic centimeter, the price of gold as $10.00 per
gram (all of them realistic values), and further assuming a year has exactly 365 days (no leap years considered) and the agreed time period is to be 2,000 years ...
What would be the better choice ? How much money would you get by the year 2000 ?
"Just imagine [tell your children, colleagues or students]: on the one side a humble, silent bank account at a modest 5% interest, gathering dust for 2,000 years, taking one full year to earn a puny $0.05,
two years for a trifle over $0.10 earning. On the other side, a massive, planet-wide cylinder of solid gold, growing to the stars at the speed of light, a humongous gold rod which will have reached to Alpha-Centaury by the time the account has accrued 22 cents, and will be a full 2,000 light-years in length by the end of the deal !"
Which option would you [they] choose ? Wanna bet ? :-)
Best regards from V.
Edited: 16 July 2004, 10:07 a.m.