__Dear Friends – Here are some answers to the problems posed in the__

**BRAINTENANCE**posting of January 25, 2010.These problems are ridiculously simple.

*Or maybe not....*

1) If you have started a savings account with $100,000.00 which accumulates interest at 4% compounded annually, after 10 years, what will be the accumulated sum in the account?

**: Using the Compound Interest Calculator, the answer turns out to be**

__Solution__**$148,024.43**. The principal amount was $100,000, the annual addition was $0.00, the years to grow were 10, the interest rate was 4%, and interest was compounded once annually.

2) Applying the same facts as in question #1, above, and assuming that inflation accumulates at a rate of 3% compounded per annum, how much would the accumulated sum in the account be worth (in the equivalent buying power of today's dollars) at the end of the ten-year period?

**: The simplest way to do it would be to use the same calculator as in the problem above, and find the total amount of “**

__Solution__*compounded inflation*” which would occur on the same principal amount at 3% annually over the 10 – year period.

Doing this gives us a compounded value of $134,391.64…this means that the amount of compounded inflation on the account is $34,391.64. If we subtract $34,391.64 (the loss due to inflation) from the compounded total in the account of $148,024.43, we are left with

**$113,632.79**. Inflation has taken its toll on our purchasing power!

**3)**Will the sum of an odd and an even number always turn out to be even or odd? (The smart answer "yes" is unacceptable).

**:**

__Solution__**Odd**. Here’s the rule: The sum of an odd and an even number will always be odd; the sum of two even numbers will always be even; and the sum of two odd numbers will always be even, as well.

**4)**Will the product obtained by multiplying an odd and an even number always turn out to be even or odd? (Again, the smart answer "yes" is unacceptable).

**:**

__Solution__**Even**. Here’s the rule: When an even and an odd number are multiplied together, the product will always be even; when two even numbers are multiplied, the product will always be even; and when two odd numbers are multiplied, the product will always be odd.

**5)**When people work together and combine their mental capabilities, the resulting "mind power" will be increased. If five collaborators are working together on the same project, what will the total mind power (expressed as a number) be if: a) the power is an arithmetic sum; b) the power is a geometric product; c) if the power is an exponential product???

**:**

__Solution__a) the power of five minds.

b) the power of 25 minds (5 x 5) or perhaps the power of 32 minds (2 x 2 x 2 x 2 x 2).

c) the power of 3,125 minds (5 x 5 x 5 x 5 x 5 x 5).

**.**

*If you believe that this is the potential power which could be generated by a mere five people working together (with 100% efficiency/ telepathy and 100% cooperation/ active thought), and others feel similarly, why do you suppose that that potential (assuming that it could be accurately measured) would very seldom, if ever, be reached? This is an open question that leads us into areas of behavioral psychology and group dynamics, but it’s very worthwhile to ponder*Faithfully,

Douglas Castle

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