Compound interest

If interest is not paid, it is added on to the capital owing.  But there becomes a time when interest should be calculated on the new, increased capital, which then includes previous interest.  Compound interest therefore recognises that interest is capitalised after a preset period.  Future interest is then charged on the new, higher capital for the next period. 

If this is repeated, with no capital repayments, the capital will grow more and more quickly.  In short, the interest increases because the capital on which it is charged increases, which then increases future interest even more.  Interest is then compounding as illustrated in Figure 2.

Figure 2
Compound interest example over three years  
£1,000 growing @ 12% per annum compounding annually, with no repayments.

 

Interest added

Capital owing

Notes

Principal

 

£1,000

Starting Capital

End of year 1

£120.00

£1,120.00

Add 12% of £1,000

End of year 2

£134.40

£1,254.40

Add 12% of £1,120

End of year 3

£150.53

£1,404.93

Add 12% of £1,254.40

Interest is added to the capital owing at the previous year-end, so it is capitalised. The following year’s interest is then charged on the higher capital amount owing at each year-end.  The total interest charged is £404.93, significantly more than the £360 shown in Figure 1.

The longer the compounding period, the more dramatic is the effect.  Over 100 years for example, an initial £1,000 at the same 12% interest rate would grow to over £83 million.  Without compounding it would worth just £13,000.  Clearly, given sufficient time, compound interest can have a surprisingly large outcome: simple interest is totally inappropriate.

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