Return, properly annualised — not what your brokerage shows you.

Three returns, all called “ROI”

The acronym “ROI” is used loosely to mean three different calculations that produce three different numbers from the same data. A diligent investor needs to know which one is being quoted in any given context.

• Simple total return. (Final value − initial investment) ÷ initial investment. Ignores time. A 50 % return is the same number whether earned in one year or thirty.
• CAGR (compound annual growth rate). The constant annual rate that takes initial value to final value over n years. The figure brokerage statements should show but mostly do not.
• IRR (internal rate of return). The CAGR equivalent for an investment with multiple cashflows in and out (monthly contributions, periodic withdrawals). The right number when the investment is not a single buy-and-hold transaction.

The calculator on this page reports all three. Simple ROI is shown in the headline. CAGR and IRR collapse into a single “annualised” figure that uses IRR when contributions are non-zero and reverts to CAGR for the no-contributions case. The math is on the formulas page.

About the reviewer — Daniel K. Lim, CFA

Experience. Daniel spent six years as an associate and senior associate at a Singapore-headquartered private-equity fund (mid-market growth-stage deals across Southeast Asia, ticket sizes US$15–75m), with a brief on performance attribution for the firm's LP reporting. He left in 2024 to set up an independent investment-analysis practice serving family offices and high-net-worth individuals across Singapore, Hong Kong, and Sydney. The IRR engine that drives this calculator is a simplified consumer-facing version of the cash-flow-aware return attribution he built for institutional reporting.

Expertise. Daniel holds the CFA charter (awarded 2019), a BBA in Finance from the National University of Singapore, and the GIPS (Global Investment Performance Standards) verification certificate. His specialisation is performance attribution: separating the realised return into its drivers (asset selection, allocation, market beta, currency) and identifying which can be replicated systematically and which depended on specific events. He is a member of the CFA Society Singapore and contributes to its continuing-education programme.

Authoritativeness. Daniel has presented at CFA Society Singapore chapter events on money-weighted vs. time-weighted return, has commented in The Business Times and Nikkei Asia on private-market valuation methodology, and serves on the editorial review panel of an industry private-markets newsletter.

Trustworthiness. Every figure produced by this calculator is verified against three independent reference implementations: the closed-form CAGR formula for the no-contribution case, an Excel IRR() + XIRR() cross-check for the contributions case, and a per-period accumulation simulation that compounds at the implied monthly rate to verify final-value reconciliation. Discrepancies greater than 0.05 percentage points block release. Daniel reviews every release. Last verified May 2026.

Why annualisation matters

Two investments produce a 60 % total return. Investment A took 4 years to do it; investment B took 12 years. Their annualised returns are 12.5 % and 4.0 % respectively — a three-fold difference. The total-return figure makes them look identical; the annualised figure shows they are very different.

The standard CAGR formula:

CAGR = (V_final / V_initial)^1/n − 1

works only when there are no intermediate cashflows. For investments with monthly contributions, you need IRR. The calculator detects this automatically: enter monthly contributions and the engine switches from CAGR to IRR via Newton-Raphson convergence on the cashflow series.

Reference: ROI translations across holding periods

What a given total return implies as an annualised CAGR for various holding periods:

A “tenbagger” (1,000 % total return) over 10 years is an annualised 27 %; the same tenbagger over 20 years is just 12.6 % — impressive but not transformational. Holding period materially changes the meaning.

Verification methodology

1. Closed-form CAGR. The textbook formula for the no-contribution case, computed in a single expression.
2. Newton-Raphson IRR. A 60-iteration converged solver for cashflow series. Converges to within 1e-9 in typical cases.
3. Excel IRR() / XIRR() cross-check. Identical inputs passed to Excel's IRR functions. Final precision compared.
4. Round-trip. The reported annualised rate is fed back through a forward-projection simulation; final value must reconcile to the user-entered final value within 0.01% tolerance.

Frequently asked questions

Should I use simple ROI or annualised return?

Annualised, almost always. Simple ROI is a curiosity for headline-only purposes; annualised return is the figure to compare across investments and against benchmarks. The exception is investments held for less than one year, where simple ROI is the natural unit.

Why is real return lower than nominal?

Inflation erodes purchasing power. A 7 % nominal return in a 3 % inflation environment is a 3.88 % real return — the actual increase in your purchasing power. For long-horizon planning (retirement, college funding, FIRE targets), real returns are the correct unit. The real return page walks through the conversion in detail.

Is the S&P 500 the right benchmark?

For a US-focused equity portfolio, yes. For international portfolios, use the MSCI ACWI or a regional index. For balanced 60/40 portfolios, blend the equity benchmark with a bond benchmark. The benchmark page covers the alternatives.