compound interest

Compound interest is the reason all fiat currencies eventually end up being worth what they are - paper (it might be electrons this time around, we'll see).

In the long history of civilised humankind, there has not been a single paper currency that has not burned over time. All money that is backed by fiat (paper currencies) end up worthless at some point.

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As an example, assume that a fiat currency actually stood the test of time and remained in circulation for 2000 years.

Just think of how much you'd have if you deposited 1 cent of this fictitious money when BC turned to AD (in other words, 0 CE) into an interest bearing account.

If the interest rate was a mere 1% pa, in the year 2000, you would have $4.3 million. Not too shabby.

If the interest rate was, say, 3% pa, by the year 2000, you'd have a something like $4.7 x 10^25. That's ... ahem ... a very big number.

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And you wonder why there hasn't been a single paper currency that has lasted near that amount of time.

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rewritten April 5th, 2002.

Compounded n times per year:

total = initial * ( 1 + rate / n ) ^{n * time}

$.01 compounded annually for 2000 years at 3% = $473 hexillion
compounded quarterly (n=4) = $913 hexillion
compounded monthly (n=12) = $1060 hexillion

Compounded continuously:

total = initial * e ^{rate * time}

$.01 compounded continuously for 2000 years at 3% = $1142 hexillion

Where rate is in decimal. (ie 9% = .09)

Compound interest becomes particularly important when planning for retirement. The golden rule here is start saving early.

Consider the following example based on an interest rate of 12%. Fred is a wise young man who starts saving £100 per month at the age of 20 and continues doing so for the next 10 years. When he reaches the age of 30 he decides to stop contributing and lets his nest egg accumulate. Joe on the other hand spends his twenties having a good time and frittering away his cash. When he hits 30 he decides to start saving for his old age and saves £100 per month for the next 30 years.

          Fred (£100pm Age 20-30)  Joe (£100pm Age 30-60)

Age 20            0                        0 

Age 30      £22,404                        0 

Age 40      £69,582                  £22,404 

Age 50     £216,112                  £91,986 

Age 60     £671,210                 £308,097 

Look at the results. Amazing isn't it? Despite contributing only 1/3 as much, Fred has accumulated over twice the amount that Joe did.