Practical guide
Investment returns and compounding
Returns on savings and investments are almost always quoted as percentages. A few simple rules explain why gains and losses are not symmetrical, why averages can mislead, and why small differences in rates or fees grow large over time.
Calculating a simple return
A return is the percentage change in value from start to finish.
Return = (ending value − starting value) ÷ starting value × 100
$1,000 grows to $1,150: $150 ÷ $1,000 = 15% return
This is the same calculation as any percentage increase or decrease, so you can use the percentage change calculator with the starting and ending values. If you received dividends or interest along the way, add them to the ending value to get a total return.
Losses need bigger gains to recover
A percentage loss and the same percentage gain do not cancel out, because the gain is measured from a smaller base. If $1,000 falls 20% to $800, a 20% gain only brings it to $960. To get back to $1,000 you need $200 ÷ $800 = 25%.
| Loss | Gain needed to break even |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 25% | 33.3% |
| 33.3% | 50% |
| 50% | 100% |
| 75% | 300% |
The formula is: gain needed = loss ÷ (1 − loss), using decimals. A 50% loss needs a 100% gain, which is why large drawdowns take so long to recover from.
Average returns can mislead
Suppose an investment gains 50% one year and loses 50% the next. The simple average of the two yearly returns is 0%, which sounds like you broke even. You did not:
$1,000 × 1.50 = $1,500 after year one
$1,500 × 0.50 = $750 after year two
Actual result: 25% loss, despite a 0% "average".
A more honest measure is the compound annual growth rate (CAGR), the steady yearly rate that would turn the starting value into the ending value.
CAGR = (ending ÷ starting)^(1 ÷ years) − 1
$10,000 grows to $16,105 over 5 years: (1.6105)^(0.2) − 1 ≈ 10% per year
How compounding works
With compounding, each period's growth is added to the balance, and the next period's growth is calculated on that larger amount. Over long periods this makes a big difference compared with simple interest, which only ever pays on the original amount.
$5,000 at 6% per year for 10 years
Simple interest: $5,000 + ($5,000 × 0.06 × 10) = $8,000
Compounded yearly: $5,000 × 1.06^10 ≈ $8,954
The extra $954 is interest earned on earlier interest. The longer the time period, the wider that gap becomes.
The rule of 72
For a quick estimate of how long it takes money to double at a steady compound rate, divide 72 by the yearly percentage rate. At 6%, 72 ÷ 6 = 12 years; the exact answer is about 11.9 years. At 9%, money doubles in roughly 8 years. The rule works best for rates between about 4% and 12%.
Small fees, big differences
Because fees are charged every year, they compound too. Compare $10,000 growing for 30 years at 7% with the same investment at 6% after a 1% yearly fee:
At 7%: $10,000 × 1.07^30 ≈ $76,123
At 6%: $10,000 × 1.06^30 ≈ $57,435
A one-point fee costs roughly $18,700, about a quarter of the result.
Adjusting for inflation
A nominal return is the headline number. A real return accounts for rising prices. You can estimate it by subtracting inflation, but the precise method divides instead:
Real return = (1 + nominal) ÷ (1 + inflation) − 1
7% return with 3% inflation: 1.07 ÷ 1.03 − 1 ≈ 3.9% real return
Important note
The examples above use fixed, made-up rates to explain the arithmetic. Real investments rise and fall unpredictably, past performance does not guarantee future results, and taxes can change outcomes significantly. This guide is educational and is not financial or investment advice. See the disclaimer for more.