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3 Years
Compound interest is a multiplier that affects the new value each time.
If the compound interest is 10% per annum, the multiplier each year is 1.1.
Year 1: $1000 * 1.1 = $1100
Year 2: $1100* 1.1 = $1210
Year 3: $1210* 1.1 = $1331
This means that it will take 3 years for $1000 to amount to $1331 at 10% per annum.
Alternatively, you can use a logarithm. The calculation can be written as:
1000 * [tex]1.1^n[/tex] = 1331, where n is the number of years.
Rearranged, this gives [tex]1.1^n[/tex] = 1331/1000 or [tex]1.1^n[/tex] = 1.331.
A logarithm can work out the value of n, and is written in the form log1.1(1.331), which gives a value of 3.