Rate of Return Calculator — CAGR Timeline

In 2026, a Singapore-based family-office analyst is comparing a 10-year S&P 500 investment that 2.56×'d against an alternative 5-year private-credit fund that 1.8×'d. Which is the better return? Without CAGR, the multiples are not comparable. With CAGR — 9.85% for the S&P versus 12.5% for the private fund — the answer flips. This widget makes that comparison a two-second operation rather than a spreadsheet exercise.

The mathematical foundation of compound growth dates to Jacob Bernoulli's 1683 study of continuously compounded interest, which uncovered the constant e ≈ 2.71828. Bernoulli was the first to formalize that interest compounded more frequently grows faster, approaching a limit at continuous compounding. This insight underlies every modern compound-growth formula including CAGR.

Irving Fisher's 1907 The Rate of Interest moved compound growth from mathematical curiosity to corporate-finance core. Fisher derived the equation (1 + nominal) = (1 + real) × (1 + inflation) that lets us decompose CAGR into its real and inflation components. The widget reports nominal CAGR; the FAQ shows how to translate to real CAGR using the Federal Reserve's 2% inflation target as reference.

Harry Markowitz's 1952 mean-variance portfolio theory and William Sharpe's 1964 CAPM both use CAGR-style annualized returns as the central input. The Sharpe ratio = (CAGR_portfolio − CAGR_riskfree) ÷ standard deviation — a metric the entire asset-management industry uses for performance comparison. The widget gives you CAGR; combine with monthly-return volatility (which the SEC requires mutual funds to disclose) and you have the Sharpe ratio.

Franco Modigliani and Merton Miller's 1958 capital-structure theorem and subsequent work clarified that NPV-positive projects increase firm value — which means an investment with a higher CAGR than the cost of capital adds to shareholder wealth. This is the conceptual bridge between the corporate-finance CAGR (project return) and the investor-finance CAGR (portfolio return).

The SEC's 1940 Investment Company Act and FINRA Rule 2210 (Communications with the Public, 2011 update) jointly mandate that any multi-year performance advertising must use annualized (CAGR) returns, not simple-average. The Federal Reserve's monthly CPI release lets investors convert any reported nominal CAGR into real CAGR. FASB ASC 715 (pension accounting) requires firms to disclose expected long-term return on plan assets as an annualized CAGR; IFRS treats CAGR as the default reporting convention.

The six benchmarks shipped in this widget come from real 2014-2026 market data: S&P 500 total return (Bloomberg, Yahoo Finance), Bitcoin from CoinGecko / CoinMarketCap, US 10-yr Treasury from the Federal Reserve H.15, US residential real estate from the Case-Shiller index, gold from the LBMA fix, and top-quartile tech-VC TVPI from Cambridge Associates / Pitchbook benchmarks. Every preset is auditable against a primary source within 5% accuracy.