Result
- Total return (on total contributed)60.00%
- Dollar gain$6,000.00
- CAGR after feessubtracting 0.10% annual fee drag9.76%
- Investment doubled in7.3 years (Rule of 72)
How to use this calculator
- Enter what you invested and what it's worth now (or sold for).
- Type how many years you held it (decimals OK — 1.5 = 18 months).
- Add the annual fees — typical index fund: 0.03-0.10%, actively managed: 0.5-1.5%.
About this tool
Two return numbers most people confuse: total return (raw % gain since you bought) and CAGR (compound annual growth rate — what your money actually earned per year on average). For investments held more than a year, CAGR is the apples-to-apples number you want. This calculator shows both, plus the brutal effect of annual fees: a 1% expense ratio over 30 years can eat 30% of your final balance. The "Rule of 72" line is a useful shortcut — divide 72 by your annual return to estimate doubling time.
How it works — the formula
Total return = (final − initial) / initial
CAGR = (final / initial)^(1 / years) − 1
IRR: rate r such that Σ CFₜ / (1+r)ᵗ = 0Total return is the simple percentage gain. CAGR (compound annual growth rate) annualizes that gain assuming smooth compound growth — useful for comparing investments over different horizons. Internal Rate of Return (IRR) is the discount rate that zeroes out the net present value of all cash flows, the standard money-weighted measure when contributions and withdrawals happen at different times.
Worked examples
- Inputs:
- initial = $10,000, final = $14,500, years = 5
- Output:
- Total return = 45.0%; CAGR ≈ 7.71%
- Inputs:
- rate = 8%
- Output:
- 72 / 8 ≈ 9 years (exact: ln(2)/ln(1.08) ≈ 9.006)
- Inputs:
- $100k for 30 years at 7% gross
- Output:
- No fee → $761,226; 1% fee (6% net) → $574,349; the fee cost ≈ $186,877
What "investment return" actually measures
Investment return is the change in the value of an investment over a period, usually expressed as a percentage. It combines two components: capital appreciation (change in the underlying asset's price) and income (dividends, interest, distributions). The sum divided by initial value gives total return.
This calculator computes projected future value from a starting balance, regular contributions, an expected annual rate of return, and a time horizon. It uses the standard compound-interest annuity-in-arrears formula: FV of initial + FV of monthly contribution stream.
Historical returns by asset class
Long-run historical return figures from academic research (Ibbotson SBBI, Dimson-Marsh-Staunton Global Investment Returns Yearbook) provide reasonable expected-return benchmarks:
| Asset class | Nominal return | Real (after inflation) | Std deviation |
|---|---|---|---|
| Large-cap US stocks (S&P 500) | 10.2% | 7.1% | 19.5% |
| Small-cap US stocks | 11.9% | 8.7% | 31.5% |
| Long-term government bonds | 5.4% | 2.4% | 9.9% |
| Intermediate government bonds | 4.9% | 1.9% | 5.6% |
| Treasury bills (cash) | 3.3% | 0.4% | 3.1% |
| US inflation (CPI) | 2.9% | — | 4.0% |
Arithmetic vs geometric mean return
Two ways to summarize a stream of returns produce different numbers. Arithmetic mean simply averages annual returns; geometric mean (CAGR — compound annual growth rate) accounts for compounding.
For a portfolio returning +50% in year 1 and -50% in year 2, arithmetic mean is 0%. But you actually LOST money: $100 → $150 → $75. Geometric mean is -13.4%. This is why long-run performance is quoted as CAGR (geometric), not arithmetic average.
The gap between arithmetic and geometric mean grows with volatility. For low-volatility bond portfolios the two are within 0.5%; for high-volatility stock portfolios the gap can be 2-3% per year over long horizons.
The tax drag on investment returns
Investment returns in taxable accounts are eroded by tax drag: dividends taxed annually (0/15/20% for qualified dividends, ordinary rates for non-qualified), interest taxed as ordinary income, capital gains realized in mutual fund distributions taxed even if you did not sell.
Tax drag on a broad-market index fund typically runs 0.3-0.7% annually — mostly from dividend and small realized-gain distributions. On a $100K balance compounding for 30 years, a 0.5% tax drag reduces the final balance by roughly $130K (~15%).
Tax-advantaged accounts (401(k), IRA, Roth IRA, HSA) eliminate this drag. The compounding advantage of tax-deferred or tax-free growth over 30+ years is one of the largest financial-planning levers available.
The impact of fees
Investment fees compound just like returns, only against you. A 1% annual fee difference over 30 years on a $100K portfolio compounding at 7% reduces the final balance from $761K to $574K — a $187K gap for what looks like a small percentage.
Modern broad-market index funds and ETFs charge 0.03-0.10% expense ratios. Older actively-managed mutual funds average 0.75-1.25%. Financial advisor fees typically run 0.5-1.5% of assets under management. Every layer of fee compounds against your return.
The Vanguard/Fidelity/Schwab index fund revolution has made single-digit-basis-point fees widely available. For most passive index investors, total portfolio expense should be under 0.15% annually — anything higher deserves specific justification.
Real vs nominal returns
Nominal returns are the raw percentage change; real returns are the nominal return minus inflation. Historical US inflation averages about 3% annually, but has ranged from -2% (deflation, 2009 briefly) to +14% (1980) in recent decades.
Long-term planning should use real returns. A "10% return" over 30 years produces very different purchasing power depending on the inflation trajectory. Modeling inflation-adjusted returns (typically 6-7% real for stocks, 1-3% real for bonds) gives more honest expected-value calculations for retirement planning and long-horizon goals.
Limitations
- CAGR smooths over volatility; two investments with identical CAGR can have very different drawdowns and risk.
- Past returns are not predictive — equity premiums vary by decade.
- Fees, taxes, and inflation are not subtracted unless you input net or real rates.
- IRR can produce multiple valid solutions when cash flows change sign more than once.
Return calculations are illustrative. This calculator does not provide investment advice — past performance does not guarantee future results, and all investing involves risk of loss.