August 18th, 2014 at 8:52:43 AM
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EFFECT OF COMPOUNDING

A 'story' for High Schools Math teachers to teach Compounding and another concept.

So, in this country banks in their efforts to attract Deposits started to incerase the interest rates they give on deposits.

Bank A gave 10%. Bank B gave 15% to steal the deposits.

Bank A increased the rate to 20% to get back the deposits. Bank B went to 20%.

And so on to 30%, 40%, 50%, 70%, 80%

Untill the Central Bank of the country intervened and set as Maximum Nominal Interest rate of 100%.

So all banks were giving 100% with no further possibility of increase to beat the competition.

Until the CEO of Bank A thought. Why not give them the Nominal of 100% interest at 6 months intervals. ie 50% per 6 months.

This way $100 will become $150 at 6 months but will become $225 in the year with the Compounding, better than the $200 with Interest at the end of the year.

So Bank A offered compounding at 6 months with 100% nominal rate and stole all the deposits.

Bank B went further with Quartely compounding and 100% nominal rate for even better return.

And the competition went like that, with Monthly Compounding, Weekly, Daily, Hourly, By Minute, By second, by 100th of a second.

Untill the CEO of a bank came and said that we offer Infinite compounding.

The Boards of Directors of the bank got confused. You can do that. Infinite Compounding means we will pay infinite Interest and we cannot pay that?

But the CEO was not worried.

So how much wil the bank pay out on a $100 for 100% Interest with Infinite Compounding.

(For the Math guys, I appreciate this is a trivial question.)

A 'story' for High Schools Math teachers to teach Compounding and another concept.

So, in this country banks in their efforts to attract Deposits started to incerase the interest rates they give on deposits.

Bank A gave 10%. Bank B gave 15% to steal the deposits.

Bank A increased the rate to 20% to get back the deposits. Bank B went to 20%.

And so on to 30%, 40%, 50%, 70%, 80%

Untill the Central Bank of the country intervened and set as Maximum Nominal Interest rate of 100%.

So all banks were giving 100% with no further possibility of increase to beat the competition.

Until the CEO of Bank A thought. Why not give them the Nominal of 100% interest at 6 months intervals. ie 50% per 6 months.

This way $100 will become $150 at 6 months but will become $225 in the year with the Compounding, better than the $200 with Interest at the end of the year.

So Bank A offered compounding at 6 months with 100% nominal rate and stole all the deposits.

Bank B went further with Quartely compounding and 100% nominal rate for even better return.

And the competition went like that, with Monthly Compounding, Weekly, Daily, Hourly, By Minute, By second, by 100th of a second.

Untill the CEO of a bank came and said that we offer Infinite compounding.

The Boards of Directors of the bank got confused. You can do that. Infinite Compounding means we will pay infinite Interest and we cannot pay that?

But the CEO was not worried.

So how much wil the bank pay out on a $100 for 100% Interest with Infinite Compounding.

(For the Math guys, I appreciate this is a trivial question.)

August 19th, 2014 at 1:31:58 PM
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Shouldn't you say "Instantaneous" compounding instead of "Infinite"? It does not actually pay anything infinite.Quote:AceTwoSo how much wil the bank pay out on a $100 for 100% Interest with Infinite Compounding.

$271.83 , or $100 * e

Reperiet qui quaesiverit

August 28th, 2014 at 11:02:03 PM
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Quote:24BingoThe "rule of 72" is a relic from the days before everyone had instant access to a good calculator.

I don't think basic comprehension is a relic. A calculator tells me that if I want to double my money in 8 years, I need an interest rate of 9.0508%

If I get 7% for 10 years then I will have 196.715% of what I began with.

I still think it is valuable to be able to instantly comprehend that the answer to the first question is roughly 9%, and the answer to the second question is about double.

I had a friend tell me she was in a financial planning seminar for professionals. The teacher said that with income tax rates at 36% that if a client wanted to take home $100K after taxes they needed to make $136K. She interrupted and said wouldn't the client have to bring home more than $150K before taxes. The teacher started screaming at her and saying that the tax rate was not 50%, and wasn't she paying attention. The teacher had no clue, nor did the other half a dozen professionals in the class. Calculators are for refining numbers, but you should still be able to estimate.

August 29th, 2014 at 12:17:47 AM
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It's a meaningless rule in practice because the true return will always be much less percentage-wise due to inflation and taxes. You have to much more than double the dollar amount to actually double your money.

With most investments these days paying 3% or less, I suggest the "Rule of Eternity"--you will never actually make a dime when the interest rate you earn is barely equal to the inflation rate. Take THAT one to the bank.

With most investments these days paying 3% or less, I suggest the "Rule of Eternity"--you will never actually make a dime when the interest rate you earn is barely equal to the inflation rate. Take THAT one to the bank.