CAGR Calculator
Calculate Compound Annual Growth Rate (CAGR) from beginning value, ending value, and time period. Measure smoothed annual investment returns.
Reviewed by Sahil, Senior Finance & Tax Editor
Calculator
Adjust values & calculateGrowth at 13.9852% CAGR
Goal Analysis at Current CAGR (13.9852%)
Future Projections from $25,000
Formula
Where Ending Value is the final investment value, Beginning Value is the initial investment value, and n is the number of years. This formula calculates the constant annual rate of return that would be needed to grow the beginning value to the ending value over the specified period, assuming compound growth.
Last reviewed: January 2026
Worked Examples
Example 1: Stock Portfolio CAGR Analysis
Example 2: Required CAGR to Reach Financial Goal
Background & Theory
The CAGR Calculator is grounded in the established principles and formulas described below. Finance and investing rest on the foundational concept of the time value of money: a dollar received today is worth more than a dollar received in the future, because present funds can be deployed to earn a return. This principle underlies virtually every valuation technique in modern finance. The future value of a present sum P growing at rate r over n periods is expressed as FV = P(1 + r)^n, while the present value of a future cash flow FV is PV = FV / (1 + r)^n. Compound growth amplifies returns significantly over long horizons, a dynamic often described as the eighth wonder of the world. Net Present Value (NPV) extends these mechanics to evaluate investment projects by summing the present values of all expected cash flows minus the initial outlay: NPV = sum[CF_t / (1 + r)^t] - C_0. A positive NPV indicates the project creates value above the required return. The Internal Rate of Return (IRR) is the discount rate that sets NPV to zero, providing a single percentage benchmark for project comparison. The risk-return tradeoff is the central tension of investment theory. Higher expected returns generally require accepting greater uncertainty. Harry Markowitz formalized this in Modern Portfolio Theory by demonstrating that portfolio variance can be reduced through diversification when assets are imperfectly correlated. The efficient frontier represents the set of portfolios offering the maximum return for a given level of risk. The Capital Asset Pricing Model (CAPM) extends this by introducing the market portfolio as a reference, defining expected return as E(r) = r_f + beta * (E(r_m) - r_f), where beta measures an asset's sensitivity to systematic market risk. Asset classes — equities, fixed income, real assets, and alternatives — differ in their return profiles, liquidity, and correlations. Strategic asset allocation determines long-run target weights based on investor objectives and risk tolerance, while tactical allocation permits short-run deviations to exploit perceived mispricings. Discount rates used in valuation models must reflect the cost of capital appropriate to the risk of the cash flows being discounted, a point stressed in corporate finance texts from Brealey, Myers, and Allen through to Damodaran.
History
The CAGR Calculator builds on a long history of ideas and practice, traced below. The formal practice of lending at interest dates to ancient Mesopotamia, where the Code of Hammurabi around 1750 BCE regulated interest rates on grain and silver loans. Banking as an institutional activity took root in medieval Italy, with merchant bankers in Florence and Venice financing trade across Europe through instruments such as bills of exchange. The Medici family operated one of the most sophisticated banking networks of the fifteenth century, pioneering double-entry bookkeeping and correspondent banking relationships. Organized equity markets emerged in the early seventeenth century. The Dutch East India Company (VOC), chartered in 1602, issued shares to the public and created the Amsterdam Stock Exchange — widely regarded as the world's first formal stock exchange. The VOC allowed investors to buy and sell shares freely, establishing the template for the joint-stock company. The period also produced the Dutch tulip mania of 1636 to 1637, one of history's first recorded speculative bubbles, in which tulip bulb futures contracts reached extraordinary prices before collapsing. England's financial revolution followed in the late seventeenth century with the founding of the Bank of England in 1694 and the development of government bond markets. The South Sea Bubble of 1720 illustrated the dangers of speculative excess and contributed to early securities regulation. Throughout the eighteenth and nineteenth centuries, industrialization created enormous demand for capital, fueling the expansion of stock exchanges in London, Paris, New York, and beyond. The New York Stock Exchange, formalized in 1817, became the world's dominant equities market by the twentieth century. The Great Crash of 1929 and subsequent Great Depression prompted the US Securities Act of 1933 and Securities Exchange Act of 1934, establishing the SEC and mandatory disclosure requirements. Harry Markowitz published his landmark portfolio selection paper in 1952, launching quantitative finance. The CAPM emerged in the 1960s through work by Sharpe, Lintner, and Mossin. John Bogle launched the first retail index fund in 1976, democratizing diversified investing and challenging active management orthodoxy.
Key Features
- Calculate compound interest and future/present value for any combination of principal, rate, compounding frequency, and time horizon to project investment growth accurately.
- Evaluate capital projects and investment opportunities using NPV and IRR analysis, with support for irregular cash flow schedules and multiple discount rate scenarios.
- Analyze portfolio risk and return by computing weighted average return, standard deviation, Sharpe ratio, and beta relative to a benchmark index.
- Compute dividend yield, payout ratio, and earnings per share to compare income-generating stocks and assess dividend sustainability.
- Calculate CAGR and annualized total return for any holding period, normalizing performance across investments with different time frames.
- Generate complete mortgage amortization schedules showing principal and interest breakdown for every payment, plus total interest paid over the loan life.
- Project retirement savings balances with configurable contribution amounts, employer match rates, annual raises, and withdrawal start dates.
- Compare after-tax returns across account types (taxable, Roth, traditional IRA/401k) to identify the most tax-efficient placement for each asset class.
Frequently Asked Questions
Formula
CAGR = (Ending Value / Beginning Value)^(1/n) - 1
Where Ending Value is the final investment value, Beginning Value is the initial investment value, and n is the number of years. This formula calculates the constant annual rate of return that would be needed to grow the beginning value to the ending value over the specified period, assuming compound growth.
Worked Examples
Example 1: Stock Portfolio CAGR Analysis
Problem:Your stock portfolio grew from $50,000 to $145,000 over 8 years. What is the CAGR?
Solution:CAGR = (Ending Value / Beginning Value)^(1/years) - 1\nCAGR = ($145,000 / $50,000)^(1/8) - 1\nCAGR = (2.9)^(0.125) - 1\nCAGR = 1.1423 - 1 = 0.1423\nCAGR = 14.23%\n\nTotal Return = ($145,000 - $50,000) / $50,000 = 190%\nSimple Average = 190% / 8 = 23.75% (overstates actual growth)\nDoubling time at this CAGR = 72 / 14.23 = 5.06 years
Result:CAGR: 14.23% | Total Return: 190% | Growth Multiple: 2.9x
Example 2: Required CAGR to Reach Financial Goal
Problem:You have $75,000 saved and want to reach $500,000 in 12 years. What CAGR is needed?
Solution:Required CAGR = (Target / Current)^(1/years) - 1\nCAGR = ($500,000 / $75,000)^(1/12) - 1\nCAGR = (6.667)^(0.0833) - 1\nCAGR = 1.1713 - 1 = 0.1713\nCAGR = 17.13%\n\nThis requires 17.13% annual compounded growth\nHistorical S&P 500 CAGR is ~10%, so this goal is aggressive\nAlternative: reduce target or increase time horizon
Result:Required CAGR: 17.13% | Growth Multiple Needed: 6.67x | Assessment: Aggressive target
Frequently Asked Questions
What is CAGR and why is it important for investors?
CAGR stands for Compound Annual Growth Rate, which measures the constant annual rate of return that would be required for an investment to grow from its beginning value to its ending value over a specified period, assuming profits are reinvested at the end of each year. Unlike simple average returns, CAGR accounts for the compounding effect and provides a smoothed annual rate that eliminates the volatility of year-to-year performance. This makes it the standard metric for comparing investment performance across different time periods, asset classes, and investment strategies. CAGR is particularly valuable because it tells you exactly what equivalent steady growth rate would produce the same final result as the actual volatile path your investment took.
How is CAGR calculated and what is the formula?
The CAGR formula is CAGR = (Ending Value / Beginning Value)^(1/n) - 1, where n is the number of years. The calculation takes three inputs: the starting value of the investment, the ending value, and the total time period. First, divide the ending value by the beginning value to get the total growth multiple. Then raise that multiple to the power of 1 divided by the number of years, which effectively distributes the total growth evenly across each year. Finally, subtract 1 to convert from a growth factor to a growth rate. For example, if $10,000 grows to $25,000 over 7 years: CAGR = (25000/10000)^(1/7) - 1 = 2.5^0.1429 - 1 = 1.1399 - 1 = 13.99%. This means the investment grew at an equivalent steady rate of about 14% per year.
What is the difference between CAGR and average annual return?
The simple average annual return adds up each year individual returns and divides by the number of years, while CAGR accounts for compounding. These can produce significantly different results. Consider an investment that goes up 100% in year 1 (from $100 to $200) and then drops 50% in year 2 (from $200 to $100). The simple average return is (100% + -50%) / 2 = 25%, suggesting strong performance. But CAGR = ($100/$100)^(1/2) - 1 = 0%, correctly showing that you ended up exactly where you started. CAGR always provides the more accurate representation of actual investment performance because it reflects what actually happened to your money, accounting for the mathematical asymmetry where losses require larger gains to recover.
What is a good CAGR for different types of investments?
Historical benchmarks provide useful context for evaluating CAGR. The S&P 500 has delivered a CAGR of approximately 10% to 11% over the past 50 years in nominal terms, or about 7% after adjusting for inflation. Individual top-performing stocks can achieve CAGRs of 15% to 25% over extended periods, though this level of outperformance is rare and difficult to sustain. Real estate investments typically produce CAGRs of 4% to 8% depending on the market and whether rental income is included. Government bonds have historically delivered 3% to 5% CAGR. Any CAGR consistently above 15% over a decade or more would be considered exceptional by professional investment standards, while anything above 20% sustained for that long would place you among the greatest investors in history.
References
Reviewed by Sahil, Senior Finance & Tax Editor · Editorial policy