Determine whether the statement is true or false. If it is...

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. Susan's salary increased from 50,000 dollar year to 60,000 dollar year over a 4 -year period. Therefore, Susan received annual increases of $5 \%$ over that period. True False

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
Susan's salary increased from 50,000 dollar year to 60,000 dollar year over a 4 -year period. Therefore, Susan received annual increases of $5 \%$ over that period.
True False

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Key Concepts

Compound Growth

Compound growth is the process whereby the value of an asset increases over time due to the effects of cumulative growth. In the context of salary or interest rates, each period's increase is applied to the new total, meaning that the growth is exponential rather than merely additive. This is crucial when determining if a fixed compound percentage rate leads to a particular result over several periods.

Effective Annual Rate

The effective annual rate is the true rate of growth or interest that accounts for the effects of compounding over a period of time. It represents the equivalent annual increase that results in the same final value when applied consistently over each period. In scenarios like these, it is used to determine the actual rate of increase when given an overall change over multiple periods.

Percentage Increase Calculations

Percentage increase calculations involve comparing an initial value with a final value to determine the proportional change between them. When this change occurs over multiple periods and is compounded, the calculation involves solving for the rate in an equation of the form (initial value) · (1 + rate)^n = (final value). This approach is essential for verifying whether a stated annual percentage increase accurately results in a specified overall change.

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