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Model compound interest or depreciation with repeated multiplication.

A percentage change each period is geometric: A=P(1±r)ⁿ, with the sign chosen for growth or depreciation.

Worked example
$1000 at 5% for two years becomes 1000(1.05)²=$ 1102.50.

Worked example
Why is 5% added twice not 10% of the original? the second 5% applies to the new balance.

Common boundary
Compound percentage change is not simple linear addition.

Compounding-frequency example: $1200$ dollars at a nominal annual rate of $6\%$ compounded monthly for two years gives $A=1200(1+0.06/12)^{24}=\$ 1352.59 $to the nearest cent. For annual depreciation replace the growth factor by$ 1-r $. To compare purchasing power with annual inflation$ i $, divide the nominal value after$ n $years by$ (1+i)^n$; nominal growth alone does not guarantee a gain in real value.