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Arithmetic Growth

TL;DR

Section titled “TL;DR”
  • Growth where the absolute change per period is constant (same amount added each step).
  • Appears as a straight line on a graph and is predictable, making planning easier.
  • Tends to be slower and less flexible than growth types with changing rates.

Definition

Section titled “Definition”

Arithmetic growth refers to growth that occurs when the rate of change is consistent and constant over a given period of time: the difference between consecutive terms is always the same.

Explanation

Section titled “Explanation”

Arithmetic growth is linear because the constant difference between consecutive terms produces a straight-line pattern on a graph. Unlike geometric or exponential growth, the rate of change does not vary or accelerate over time, so values increase by the same absolute amount each period. This consistency makes arithmetic growth straightforward to calculate and forecast.

Examples

Section titled “Examples”

Simple interest on a savings account

Section titled “Simple interest on a savings account”

An individual deposits 100intoasavingsaccountthatearns5100 into a savings account that earns 5% interest per year. In the first year, the account earns 5 in interest, resulting in a total balance of 105.Inthesecondyear,theaccountagainearns105. In the second year, the account again earns 5 in interest, resulting in a total balance of 110.Thispatterncontinues,withtheaccountearning110. This pattern continues, with the account earning 5 in interest each year, producing linear growth.

Town population

Section titled “Town population”

A town has a population of 1,000 people and grows by 100 people each year. In the first year, the population increases to 1,100 people. In the second year, the population increases to 1,200 people, and so on. This linear pattern is an example of arithmetic growth.

Stock price

Section titled “Stock price”

A stock is currently trading at 50pershareandisexpectedtoincreaseby50 per share and is expected to increase by 5 per year. In the first year, the stock price increases to 55pershare.Inthesecondyear,thepriceincreasesto55 per share. In the second year, the price increases to 60 per share, and so on. This linear increase illustrates arithmetic growth.

Use cases

Section titled “Use cases”
  • Planning and budgeting, because the constant rate of change is easy to calculate and account for.
  • Making decisions about investments, savings, and other financial planning where predictable, fixed increments are assumed.

Notes or pitfalls

Section titled “Notes or pitfalls”
  • Arithmetic growth is generally slower than growth types with changing or accelerating rates, which may be insufficient to keep pace with inflation or other economic factors.
  • It can be less flexible: the constant increment may not adjust quickly to market changes or shifts in conditions.
Section titled “Related terms”
  • Geometric growth
  • Exponential growth
  • Linear (linear growth)