# CAGR ## What is CAGR? CAGR of something [[Geometric progression]] ratio that provides a constant rate of return over the time period ## Derivation $ \begin{align} \text{End Value} &= \left(\text{Start Value}\right) (1 + \text{CAGR})^n \\ \frac{\text{End Value}}{\text{Start Value}} &= (1 + \text{CAGR})^n \\ \left(\frac{\text{End Value}}{\text{Start Value}}\right)^{\frac{1}{n}} &= (1 + \text{CAGR}) \\ \text{CAGR} &= \left(\frac{\text{End Value}}{\text{Start Value}}\right)^{\frac{1}{n}} -1 \end{align} $ ## Why is This Even a Though? (Motivation) CAGR is the **rate at which an investment grows annually** over a specified period, assuming the profits were reinvested. It represents the **smoothed annual rate of growth** from the beginning value to the ending value, making it useful for understanding the growth trajectory of an investment, even if that growth has been volatile year to year. ## Key Phrases compound rate, growth trajectory, consistent annual growth ## Resources - [CAGR explained](https://www.youtube.com/watch?v=F2mlD8Sf-fM) - [연평균 성장률 - 위키백과, 우리 모두의 백과사전](https://ko.wikipedia.org/wiki/%EC%97%B0%ED%8F%89%EA%B7%A0_%EC%84%B1%EC%9E%A5%EB%