e” – where Finance meets Science

Many of you would know I am  a trained accountant.  Most would not know that my original training was in science and engineering.  It’s that aspect of my life the I would like to write about now.

All of you would however be familiar with the concept of interest rates.  A nightly topic on the news, interest rates determine how much spare cash we have after the mortgage payment.  And the total mortgage paid is a simple calculation.  To save time, I’m going to skip the math…  but the formula is:

FV = PV(1+r)^t

Where:

FV = Future value

PV = Present Value

r  =  Interest Rate

t  = time

its the formula for calculating the total amount you pay – and, (just like me), its not very sexy!

The Cool Thing though, is if you have a greedy banker!!

…whose interest rate is high…. really high…. In fact his demands are unreasonable… 100% !! But kindly he also increases the time to pay proportionally, and reduces the interest rate charged proportionally. For simplicity lets assume PV = \$1.00 in this case.

So,

FV = (1+1/n)^n

The table below exhibits the results:-

1 year = 2 times

2 years….. 2.25 times

4 years….. 2.44 times

Perhaps, worthy of further investigation.

50 years …. 2.69159 times

10,000 years…. 2.71815 times

10,000,000 years…. 2.71828 times

As you can see our, “Greedy Banker”, gets a “diminishing return” on his investment over time… even over 10 million years – time hardly effects the total amount paid.

As the years increase the total settles to around 2.71828 times  – termed “e” – it is the base of Natural Logarithms. A key number that is used to calculate everything from life expectancy, to the curve on a suspension bridge, to a satellite’s orbit….

It still amazes me that such simple financial concept produced one of the Universe’s most useful numbers!

“e” is truly where finance and science meet!