Dirty tricks and the need to always check the truth and veracity of something

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It is not well known that the commoner populace is commonly fooled and tricked with malicious intent. The usual reason for this is said to be because someone somewhere is ripping us off. I have found that this is not all of the reason. My observation is that many times the reason is because that someone somewhere is also psychotic and gets a kick and an ego boost out of the feeling that s/he is smarter than everybody else. My evidence for this is everywhere, from Wiki's to commercial contracts to everything else.

The lesson that this tells us is that we need to put whatever systems in place to ensure that this form of corruption is annihilated. One of these systems is our own awareness of these problems and that we need to be vigilant of these probabilities. To support this we need to have the knowledge to assess whether something is a lie and dirty trick. This can only come about through education and experience.

Some of these tricks have appeared in our educational textbooks. I discovered this when I was studying economics and our economic textbooks were rife with lies and misinformation whose intention was to make us give away our assets and have them stolen from us.

One example I found was in the accounting textbooks. This was in a short formula to derive the Net Future Value (and Net Present Value) of an annuity or compounding investment eg a payment of interest on a investment - the simplest model being something like a investment at time 0 and then interest paid at the end of a time period, that interest then reinvested and then the initial principle and that interest then receiving again interest after an equally long time period etc.

The DIRTY TRICK
The actual formula for Future value is
FV = PV(1 + r)^t
FV = Amount returned in the future
PV = Amount initially invested now
r = interest (|r| < 1) t = total number of periods for which interest is due to be paid. This formula is expanded by using the binomial number theorem (or Pascal's triangle). For instance if the investment is for 3 years then we get an expansion of this as
FV = PV( (1^t + (3 x 1² x r¹) + (3 x 1¹ x r²) + (r³) )
For example, if t = 3 years, PV = 1 and r = 0.1 then
FV = PV(1 + r)^t
= 1 x (1 + 0.1)³
= 1 + (3 x 0.1¹) + (3 x 0.1²) + (0.1³)
= 1.331
ie an investment of $1 will return $1.333 dollars after 3 years with 10% interest on the initial investment.

My accounting book then stated that there is another formula for obtaining the future value of a compounding investment. This formula was meant to be used for very long term compounding investments to make calculation of future value easier. The formula is given below:

FV_{dirty trick} = PV ( (1-r^t) / (1-r) )
FV_{dirty trick} = Amount returned in the future using a dirty trick calculation of future value
PV = Amount initially invested now
r = interest (|r| < 1) t = total number of periods for which interest is due to be paid. If we say t = 3, r = 0.1 and PV = 1 then this gives us FV_{dirty trick} = PV ( (1-r^t) / (1-r) )
= 1 x (1 - 0.1³) / (1 - 0.1)
= 1 x 0.999 / 0.9
= 1.11
ie The dirty trick gives us back $0.221 less than what we should have received.

The accounting textbook that stated this is a common one that is used in Universities all over the world to teach accounting.

In general, the reason why FV > FV_{dirty trick} is because
(1 + r)^t > ((1-r^t)/(1-r))
This is because
((1-r^t)/(1-r)) = (1 + r¹ + r² + r³ + ... + r^t) ≠ (1 + r)^t