Investment Return Calculator
Calculate the total return and the annualized return (CAGR) of a single investment from its start value, end value and holding period.
Updated Formula covered by automated tests
Give this calculator what you put in, what the investment is worth now (or what you sold it for) and how many years you held it. It returns two different answers to “how did it do?”: the total return over the whole holding period, and the annualized return, also called the compound annual growth rate or CAGR.
The two are easy to mix up and are often quoted interchangeably in conversation. A fund that rose 50% over five years did not earn 10% a year; it earned about 8.4% a year, compounded. Annualizing puts a two-year holding and a nine-year holding on the same per-year footing, so you can compare them with each other, with a savings account rate, or with an index.
The formula
- V_start
- Amount invested at the start, in any currency
- V_end
- Value at the end of the period, including reinvested dividends if you want total return rather than price return
- t
- Holding period in years; fractions are allowed, so 18 months is 1.5
CAGR answers a specific question: what single, steady yearly rate would turn the starting amount into the ending amount over t years? Since growth compounds, the ending value equals V_start × (1 + CAGR)^t, and solving for CAGR gives the t-th root of the growth ratio, minus one.
The simple average, total return divided by years, is shown only for contrast. Over periods longer than a year it sits above CAGR for gains and makes losses look milder than they were, because it ignores that each year’s growth also applies to the previous years’ growth. CAGR describes the smoothed path; the actual year-by-year returns may have swung widely around it.
Worked example
In 2020 Alex put $10,000 into an index fund with dividends reinvested. Five years later the account shows $15,000.
- 1 Gain: $15,000 − $10,000 = $5,000.
- 2 Total return: $5,000 ÷ $10,000 = 0.50, or 50% over five years.
- 3 Growth ratio: $15,000 ÷ $10,000 = 1.5.
- 4 Annualize: 1.5^(1 ÷ 5) = 1.5^0.2 = 1.0845, so CAGR = 8.45% a year.
- 5 Check: $10,000 × 1.0845⁵ = $15,000, while the simple average of 50% ÷ 5 = 10% would overstate the yearly rate.
Result: Alex’s investment returned 50% in total, equivalent to a compound annual growth rate of about 8.45% per year.
Before you rely on the result
- Valid only for a single lump sum with no deposits or withdrawals between the start and end dates.
- CAGR hides volatility: two investments with the same CAGR can have had very different drawdowns along the way.
- Past returns do not predict future returns. This is a measurement tool, not investment advice; for portfolio decisions consider a fee-only financial adviser.
Frequently asked questions
Should I compare funds by total return or by CAGR?
Use CAGR whenever the holding periods differ. A 40% total return over 8 years (about 4.3% a year) is weaker than a 25% return over 3 years (about 7.7% a year), even though 40 is the bigger number. For identical periods, the two rankings agree.
What if I added money along the way?
Then this simple formula will mislead you, because new deposits inflate the ending value without being investment gains. You need a money-weighted return (an internal rate of return, the XIRR function in spreadsheets) or a time-weighted return, which is what fund companies publish.
Why does a short holding period show a huge annualized number?
Annualizing assumes the same pace continues all year and compounds. A 5% gain in one month annualizes to roughly 80%. That figure says nothing about what will happen next; for holdings under a year, the total return is the more honest number to quote.
Does this account for inflation or taxes?
No, it is a nominal, pre-tax return. To get an approximate real return, divide (1 + CAGR) by (1 + average inflation) and subtract 1. Taxes on dividends and on the gain when you sell reduce what you actually keep.
Sources
- Investor.gov (SEC): Compound interest calculator (investor.gov)