Back to Compound Growth & CAGR
11+investment-universe

CAGR explained

Understand why example: +100% then −50% = arithmetic average of +25% but CAGR of 0% (you start at 100, double to 200, halve back to 100).

In this lesson

CAGR explained is part of Compound Growth & CAGR. This preview shows how investment-universe connects to everyday family decisions such as earning, saving, spending choices, goals, approvals, or parent-guided money conversations inside Progress Penguin.

Think about this money choice

Imagine this situation: Your investment: Year 1: +30%, Year 2: −15%, Year 3: +20%, Year 4: +10%.

How it works

Example: +100% then −50% = arithmetic average of +25% but CAGR of 0% (you start at 100, double to 200, halve back to 100). The average suggests 25% growth; CAGR correctly shows you gained nothing. CAGR is the honest metric because it reflects what your actual compound growth was.

Apply it to a real decision

Real-life money moment: Your investment: Year 1: +30%, Year 2: −15%, Year 3: +20%, Year 4: +10%. What is the CAGR over 4 years if you started with 100000 in local currency and ended with 145530 in local currency? The key lesson is: CAGR (Compound Annual Growth Rate) = (ending value/starting value)^(1/years) − 1.

Activity preview

Connect the ideas

Use the lesson to complete this short practice activity.

Try one real money action

Open Tasks and submit proof for one task, or open Requests and make a deposit request. Parent approval can happen later.

Quiz preview

CAGR is:

Cash And Gold Rate
Country And Gov Rate
Cycle And Growth Range
Compound Annual Growth Rate

Your investment: Year 1: +30%, Year 2: −15%, Year 3: +20%, Year 4: +10%. What is the CAGR over 4 years if you started with 100000 in local currency and ended with 145530 in local currency?

CAGR = (145,530/100,000)^(1/4) − 1 = 1.4553^0.25 − 1 ≈ 9.8% — the actual compound growth rate, NOT the average of annual returns
CAGR is (30−15+20+10)/4=11.25% under normal conditions in practical terms
CAGR = 145,530 − 100,000 = 45,530 in this situation as a reliable approach
CAGR cannot be calculated with negative years over the longer term given the circumstances