CAGR and Inflation Explained: Growth, Prices and Real Returns
Two numbers decide whether money grows in a way that matters: how fast it grows, and how fast prices rise. Compound annual growth rate describes the first. Inflation describes the second. Comparing them shows what actually happened to purchasing power.
What CAGR measures
The compound annual growth rate is the single steady yearly rate that would take a value from its start to its end over a number of years. The formula is (end ÷ start)1 ÷ years − 1. Suppose 10,000 grows to 16,000 over five years:
- Divide the end by the start: 16,000 ÷ 10,000 = 1.6.
- Take the fifth root, which is the same as raising to 0.2: 1.60.2 = 1.0986.
- Subtract 1: 0.0986, or 9.86% a year.
- Check: 10,000 × 1.09865 returns 16,000.
The CAGR Calculator performs the same calculation, and the Compound Interest Calculator shows what a chosen rate produces year by year.
Why CAGR is not an average
An average of yearly changes ignores compounding, and that can hide a loss entirely. Suppose a value rises 50% in one year and falls 50% in the next:
- Start at 100. A 50% rise takes it to 150.
- A 50% fall takes 150 down to 75.
- The simple average of +50% and −50% is zero.
- The CAGR is (75 ÷ 100)1/2 − 1 = 0.8660 − 1 = −13.4% a year.
The value is 25% below where it started, and CAGR is the figure that says so. Volatility costs money even when the average looks flat.
What inflation does to money
Inflation reduces what each unit of currency buys. At 3% a year, a basket costing 100 today costs 100 × 1.0310 = 134.39 in ten years. Read the other way, 100 in ten years buys what 100 ÷ 1.3439 = 74.41 buys today.
The effect compounds quietly. A rate that looks small over one year becomes a large change over a decade, which is why long plans should use a realistic inflation figure rather than zero. The Inflation Calculator shows the year-by-year path for any rate you enter.
Real return: growth after inflation
A headline return tells you how the balance grew; a real return tells you how purchasing power grew. Divide the growth factor by the inflation factor and subtract 1. If an investment grows 7% while prices rise 3%:
- Growth factor: 1.07. Inflation factor: 1.03.
- Divide: 1.07 ÷ 1.03 = 1.0388.
- Subtract 1: 0.0388, or about 3.88%.
- The quick subtraction 7% − 3% = 4% is close, but it overstates the result.
Taxes and fees come out of the nominal return before inflation is removed, so the real figure can be lower again. The ROI Calculator shows the nominal percentage gain on an investment.
The same 100 at 3% inflation
Each column applies the rate for the whole period, not year by year in simple steps.
| Years | Price of today's 100 |
|---|---|
| 1 | 103.00 |
| 5 | 115.93 |
| 10 | 134.39 |
| 20 | 180.61 |
| 30 | 242.73 |
Prices more than double over 30 years at 3%, which is why a sum kept in cash loses purchasing power even though the number on the statement does not fall.
Nominal growth against real growth
The gap between the two rates widens as inflation rises. Each row divides the growth factor by the inflation factor.
| Growth | Inflation | Real return |
|---|---|---|
| 5% | 2% | 2.94% |
| 6% | 4% | 1.92% |
| 7% | 3% | 3.88% |
| 8% | 3% | 4.85% |
| 10% | 5% | 4.76% |
A 10% return with 5% inflation is worth less in real terms than an 8% return with 3% inflation, even though the headline number is higher.
Scenarios beat predictions
Nobody knows future inflation or returns. Run a low, a medium and a high case, then check whether the plan still works in the low case. A plan that only survives the optimistic scenario is not a plan but a hope.
Keep the units consistent: if the growth rate is annual, the inflation rate must be annual too, and the number of years must match both. Mixing a monthly rate with an annual period is the most common way a sensible calculation produces a strange answer.
Mistakes that distort the comparison
- Averaging yearly returns. Use the geometric path; CAGR already does it.
- Subtracting inflation without dividing. The shortcut is close only for small rates.
- Mixing monthly and annual rates. Convert one to the other before comparing.
- Ignoring taxes and fees. They reduce the nominal return before inflation is removed.
- Using one scenario. A range shows how sensitive the result is to the assumptions.
Frequently asked questions
10,000 grows to 16,000 in five years. What is the CAGR?
9.86% a year, from (16,000 ÷ 10,000) to the power of one fifth, minus 1. The factor 1.6 becomes 1.0986.
Why is the CAGR of +50% then −50% negative?
Because the value ends at 75% of its start. The square root of 0.75 is 0.866, so the CAGR is about −13.4% a year even though the simple average is zero.
If inflation is 3%, what will 100 buy in ten years?
About 74.41 of today's money, because prices rise to 134.39. The purchasing power falls by roughly a quarter.
Is the real return just growth minus inflation?
It is close for small rates but not exact. Subtract for a quick estimate, then divide: (1.07 ÷ 1.03) − 1 = 3.88%, not 4%.
- CAGR Calculator – Find the steady yearly growth rate between two values.
- Inflation Calculator – See how inflation changes prices and purchasing power.
- Compound Interest Calculator – Estimate investment growth with compound interest.
- ROI Calculator – Calculate return on investment.
More guides
- How to Calculate Percentages: 3 Methods and the Mistakes to Avoid
- Understanding Compound Interest: Why Time Matters More Than Amount
- How Loan Payments Work: Principal, Interest and the Cost of Time
- Browse all guides
This guide is for general information and is not financial, tax, legal or medical advice. See our disclaimer.