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.

Today’s money mission

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

What you need to know

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.

Real-life example

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.

Progress Penguin connection

Open the investment simulator and enter a start value of ₦100,000 and an end value of ₦250,000 over 5 years. Calculate the arithmetic average annual return (30%, 20%, −10%, 40%, 20% = 20% average). Now calculate the CAGR. Notice they are different. CAGR reflects what actually happened to the money.

Activity preview

Try the money challenge

Run the investment model and test: example: +100% then −50% = arithmetic average of +25% but CAGR of 0% (you start at 100,. Adjust one variable — time, rate, or amount — and note which has the biggest effect on the final balance.

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