The ROI formula, and what belongs in “cost”
ROI = (amount returned − amount invested) ÷ amount invested × 100. Turn 10,000 into 15,000 and that is a 5,000 net gain on a 10,000 outlay, a 50% return. The result is a ratio, so it is comparable across investments of very different sizes — which is exactly what makes it easy to misuse.
Fees belong on the cost side, not subtracted from the return, because they were money you had to put up. With 500 of commission the same trade is (15,000 − 10,000 − 500) ÷ (10,000 + 500) × 100 = 42.86%. The seven-point gap between 50% and 42.86% is what brokerage, platform, management and transaction fees quietly take.
Everything that came back belongs in the return: sale proceeds, dividends and interest received, rent collected, a tax refund attributable to the investment. Everything you paid belongs in the cost: purchase price, commissions, renovation, carrying costs. The formula is trivial; getting these two lists right is the whole job.
ROI vs annualized return (CAGR)
ROI says nothing about time. A 50% total return is excellent in one year and mediocre over ten, so fill in the holding period and the tool also gives the annualized figure: CAGR = (returned ÷ cost)^(1 ÷ years) − 1.
- 50% over 1 year — 50.00% a year
- 50% over 3 years — 14.47% a year
- 50% over 10 years — 4.14% a year
The annualized number is always lower than a simple “50 ÷ 10 = 5% a year”, because each year’s gain compounds on the last: 4.14% earned ten times over is what produces 50%, not 5%. When you compare an investment against a savings account or a mortgage rate, the annualized figure is the one to use — those are quoted per year too.
Two cases where annualizing misleads
Under a year, annualizing extrapolates. A 10% gain in six months annualizes to 21%, which assumes you can repeat the same performance immediately — usually the least defensible assumption in the whole calculation. The tool shows the figure but flags any holding period shorter than a year, because a headline like “21% annualized” from six weeks of trading is how people talk themselves into concentration risk.
For a total loss, the annualized figure does not exist. CAGR takes a real root of returned ÷ cost, and if nothing came back — a return of zero or less — no real root exists, so the tool says the annualized return is undefined instead of printing NaN or a fake −100%. Partial losses annualize normally: 10,000 down to 8,000 over two years is a −20% ROI and −10.56% a year.
ROI, IRR, ROAS and payback — which one answers your question
- ROI answers “how much did this make relative to what it cost”. It ignores when the money moved, so it is right for a single outlay and a single return and wrong for anything with a stream of cash flows.
- IRR (internal rate of return) answers the same question when money goes in and out repeatedly, by finding the rate at which all discounted flows net to zero. A rental property with irregular capital expenditure needs IRR, not ROI.
- ROAS (return on ad spend) is revenue ÷ ad spend, a gross ratio, so a ROAS of 4 can still be a loss once cost of goods is deducted. ROI on the same campaign uses profit, not revenue, and is the number that decides whether to keep spending.
- Payback period answers “when do I get my money back” — cost ÷ annual cash flow. It says nothing about what happens afterwards, so it is a risk screen rather than a profitability measure.
This page computes ROI and its annualized form. If your situation has more than one inflow or outflow, aggregate them into a single total cost and a single total return before entering them, and know that you have thrown away the timing information.
The Investment growth tab: projecting forward
The second tab answers the opposite question — not what a finished investment returned, but what a monthly savings plan is likely to become. It uses FV = P(1+i)^N + PMT × ((1+i)^N − 1) ÷ i with i = annual rate ÷ 12 and N = years × 12: monthly compounding, deposits at the end of each month, both fixed.
Start from nothing, put in 500 a month at 7% for 20 years and you reach 260,463.33 having contributed 120,000 — a 117% total return on the money you actually paid in. The year table shows contributions, gain and balance for every year, so you can see the point at which the gain overtakes the deposits.
If you need a different compounding or contribution frequency, beginning-of-period deposits, or an inflation-adjusted result, use the compound interest calculator instead — this tab keeps its inputs deliberately short. Limits here are a rate from −100% to 200% and a term up to 80 years; a plan that runs the balance below zero stops and reports the year it happened.
Worked examples by situation
- A share purchase. Bought for 10,000, sold for 15,000 after 3 years, with 500 of total commission and 300 of dividends collected. Cost 10,500, returned 15,300 → 45.71% ROI, 13.37% a year. Forgetting the dividends would have cost you nearly three points.
- A rental year. 300,000 property, 12,000 of rent collected, 3,600 of tax, insurance and repairs. For the annual yield enter 300,000 invested and 308,400 returned with a 1-year period: 2.8%. That is the unlevered yield; a mortgaged purchase has a much smaller cash outlay and a very different number.
- A marketing campaign. 8,000 spent, 30,000 of revenue, 18,000 of cost of goods. ROAS is 30,000 ÷ 8,000 = 3.75, but the ROI uses profit: (30,000 − 18,000 − 8,000) ÷ 8,000 = 50%. Both are true; only one tells you whether to spend more.
- A course or certification. 3,000 in fees plus 100 hours of your time; a 4,000 annual pay rise. Counting only the cash, the first year is 33% and every year after that is pure gain — which is why training usually beats financial investments on ROI and loses on liquidity.
What ROI leaves out
Risk, above all. A 12% return from a government bond and a 12% return from a single small-cap stock are the same number and not the same outcome; ROI has no way to say so. It also says nothing about liquidity — a property at 40% you cannot sell for a year is not comparable to a fund at 40% you can exit tomorrow.
Tax and inflation are outside the calculation too. Korean domestic stock gains are largely untaxed for retail investors while overseas gains face 22% above the annual deduction; either way, enter after-tax amounts if you want the return you keep. And a 5% nominal return in a 4% inflation year is barely a 1% real gain — the compound interest calculator has an inflation field for exactly this.
Finally, opportunity cost. A positive ROI is not automatically a good decision — it has to beat what the same money would have done elsewhere, including simply repaying debt, where the guaranteed return equals your loan rate.