How compound interest is calculated
Result = Capital × (1 + r)ⁿ, where r is the return per period and n is the number of periods. Each period's profit stays in the account and earns on its own in the next period. If you add C at the end of every period, the result grows by C × ((1 + r)ⁿ − 1) / r. Without reinvesting, profit is withdrawn, the capital grows only by deposits, and the result is the capital plus the withdrawn profit.
| Example | With reinvesting | Without reinvesting |
|---|---|---|
| 1,000 at 5% a month, 12 months | 1,795.86 | 1,600 |
| 1,000 + 100 a month at 2% a month, 24 months (3,400 invested) | 4,650.62 | 4,432 |
| 10,000 at 20% a year, 10 years | 61,917.36 | 30,000 |
Monthly and annual return
Monthly percentages are not added but multiplied: annual = (1 + r)¹² − 1. 3% a month is 42.58% a year, 5% a month is 79.59%, not 60%. The reverse calculation is in the second block of the calculator: to double an account in 12 months you need 5.95% a month.
The rule of 72
A quick estimate of doubling time: 72 / return in percent. At 5% a month — 14.4 months, exactly — 14.2. The rule is most accurate around 8% per period; at higher rates the error grows, so the calculator shows both values.
What the calculator won't tell you
- Trading returns are not smooth. +50% and then −50% give −25%, although the «average» is zero. The bigger the swings, the lower the real growth at the same average return — see «Compound interest in trading».
- Drawdowns cost time. After −30% you need +42.9% to get back to the peak; the drawdown calculator shows the recovery.
- High returns mean high risk. «10% a month» almost always means a risk level at which the chance of blowing the account within a year is high: check it in the risk of ruin calculator.
How Davinchu calculates it
In account analytics «Growth» is compounded by year and «Abs. growth» is simple; deposits and withdrawals are not counted as income. Next to it are monthly returns and yearly totals, so you see what the account really earns rather than what a calculator would promise. How to measure return with deposits — in «Portfolio return with deposits». The Free plan connects two accounts at no cost.