Saturday, 3 January 2009

2.7182... and the meaning of e

The year 2009 promises to be a very interesting one as far as banks and credit are concerned. The banks have been bailed out by government but they have not been so keen to pass on their good fortune to other less powerful industries. On Monday of this coming week the last Woolies shop will close its doors and others such as Adams have gone into receivership. How many more before the end of the this year?... well only time will tell.

Entwhistle, or "The Prof" as one of our more distinguished club members is known, was muttering about 'exponential increases' and other mathematical terms that had some members hot under the collar. "what is all this exponential stuff about?" asked Carruthers blithely.

The Prof looked at him as though he were addressing an ignorant student. "There are two mysterious numbers. One is pi and the other is e. Pi = 3.14159... and e = 2.7182... Most people know about the first but have not heard much about the second.

"Look has this got anything to do with banking?" asked Carruthers.

"Oh quite a bit," said the Prof, "if you will just give me a moment of your time.

"Is it going to affect my savings?" interjected Manton.

"Well if will affect how you understand them. For instance suppose you borrow £1 and suppose the interest rate is 100% per annum."

"Bit steep isn't it?"

"You wait until next year!" shouted someone from the back. "It won't be far off that!"

"Anyway," said the Prof, ignoring the interruptions. "After one year you owe £1 borrowed plus £1 interest making £2 in all."

"That clear enough," said Carruthers.

"Yes but the bank wants to get more than that. And it can do it by not putting up the interest rate."

"How can it do that?"

"Simply by spreading the interest out over a number of payments and making it compound." People looked perplexed so he continued. "Look, if they split the interest to two payments of 50% every six months what would you pay then?"

"The same."

"No. You would owe £1 borrowed plus £0.50 first interest plus £0.75 second interest equals £2.25 total. Which is the same as (1+1/2)2 It compounds because you owe £1.50 after the first six months and so interest is more. Not a bad way to earn even more."

"The banks know all the tricks," said someone.

"And if you make the interest monthly, then that becomes (1+1/12)12 = 2.6130 which you end up owing."

"It gets more every time."

"Exactly. and if they could make it daily interest you would be paying (1+1/365)365 = 2.71457. Of course if you paid interest at smaller and smaller intervals you would pay more, but there is a limit and that limit is 2.7182 which is exponential number that is given the symbol e. If you take 1000 intervals you get 2.7169, and if you take an infinte number you end up with e. Strange isn't it? It is one of those special beautiful numbers that are always turning up in mathematics. It can't be expressed as an exact fraction, just like pi, but it is important never the less."

"Is it going to help us with the credit crunch Prof?"

"I doubt it very much. But it will help you with your calculus problems." The Prof looked very pleased with himself. But no one else did. He always did go off on a tangent.

"Happy new year, Prof!"

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