Compound Interest - Applications in Growth and Depreciation

Growth: This refers to the increase in a quantity over a period of time, such as the increase in the population of a city or the appreciation of land value. Visually, growth is represented by an upward-sloping curve where the slope becomes steeper over time because the increase is calculated on the already increased value of the previous year.

Depreciation: This is the reduction in the value of an asset, such as a car, computer, or machinery, due to wear and tear or age. On a graph, depreciation appears as a downward-sloping curve that starts high and gradually levels out, reflecting that the value decreases by a percentage of its current (reduced) value each year.

The Initial Value ($P$): In these applications, the starting population or the original cost of an item is treated as the Principal ($P$). This is the baseline from which growth or decay is measured.

Rate of Change ($R$): This is the constant percentage at which the value increases (Growth Rate) or decreases (Depreciation Rate). For growth, the rate is positive, and for depreciation, it is negative.

Time Period ($n$): This represents the number of years or intervals over which the growth or depreciation occurs. It acts as the exponent in our calculations, representing the number of times the rate is applied.

Variable Growth/Depreciation: Sometimes the rate of growth or depreciation is not constant. If a value grows at $R_1\%$ in the first year and $R_2\%$ in the second year, the final value is calculated by applying these rates successively like a chain reaction.

Scrap Value: In depreciation problems, the value of an item after its useful life is often called the scrap value. This is the final amount ($V$) after $n$ years of depreciation.