In short. Compound interest means the profit stays in the account and the next return is earned on it too. The formula is result = capital × (1 + r)^n, where r is the return per period and n is the number of periods. $1,000 at 5% a month grows to $1,795.86 in a year with reinvestment and to $1,600 without it. Trading returns are never smooth, though: swings, drawdowns and excessive risk eat into growth, so a «flip your account» table at 10% a month is arithmetic, not a plan.
The formula with and without reinvestment
Without reinvestment (simple interest) the profit is taken out and every return is earned on the original amount: result = capital × (1 + r × n). With reinvestment the profit keeps working: result = capital × (1 + r)^n.
Example: $1,000, 5% a month, 12 months. Simple: 1,000 × (1 + 0.05 × 12) = $1,600. Compound: 1,000 × 1.05^12 = $1,795.86.
A real account earns a different return each month: result = capital × (1 + r₁) × (1 + r₂) × … × (1 + rₙ). A monthly return converts to an annual one as (1 + r)^12 − 1, and an annual one to monthly as (1 + R)^(1/12) − 1: 50% a year is 3.44% a month, not 50 / 12 = 4.17%.
In Excel: =1000*(1+5%)^12 or =FV(5%,12,0,-1000) — both return 1,795.86. The amount you invest goes into FV as a negative number: per Microsoft's help, cash you pay out is negative.
Table: $1,000 at 2, 5 and 10% a month
| Per month | Per year | 12 months | 24 months | 36 months | 36 months, no reinvestment |
|---|---|---|---|---|---|
| 2% | 26.8% | $1,268 | $1,608 | $2,040 | $1,720 |
| 5% | 79.6% | $1,796 | $3,225 | $5,792 | $2,800 |
| 10% | 213.8% | $3,138 | $9,850 | $30,913 | $4,600 |
Amounts are rounded to the dollar. The gap with simple interest widens every period. Your own case — with deposits and withdrawn profit — is in the compound interest calculator.
Why almost nobody sustains «10% a month»
10% a month is 1.1^12 − 1 = 213.8%, or about 214% a year. In five years $1,000 would become $304,482, in ten — $92.7 million. Three things stand in the way:
- Risk. 10% a month takes a large risk on every trade, and drawdowns grow with it — the numbers are below.
- Uneven months. After one −30% month you need +42.9% to get back — almost four months at 10%.
- Hidden risk. A smooth high-return curve is often drawn by grids and martingale: months of calm, then the deposit goes in one strong move. See «Grid EAs and martingale: how to calculate the risk».
Volatility eats growth
+50%, then −50%: $1,000 → $1,500 → $750. The arithmetic mean of the two months is 0%, yet the account is down 25%. The real growth rate is the geometric mean: √(1.5 × 0.5) − 1 = −13.4% per period.
Two strategies, both averaging +5% a month. The first makes exactly +5% every month — +79.6% for the year. The second alternates +20% and −10% — (1.2 × 0.9)^6 − 1 = +58.7% for the year, or 3.92% a month. A handy approximation is geometric ≈ arithmetic − σ² / 2, where σ is the standard deviation of returns: 5% − (15%)² / 2 = 3.875%.
In trade statistics these are AHPR (the arithmetic mean return per trade) and GHPR (the geometric mean); the account grows at the GHPR rate. More in «Sharpe ratio, Z-score, AHPR and GHPR explained».
Drawdown and recovery
Compounding works in reverse as well: after a drawdown D you need D / (1 − D) to get back. That is +11.1% after −10%, +25% after −20%, +42.9% after −30% and +100% after −50%. It also costs time: at 5% a month recovering from −50% takes ln 2 / ln 1.05 ≈ 14.2 months, at 2% — 35 months.
Formulas and common mistakes are in «How to calculate account drawdown», and the drawdown calculator shows the recovery for your own drawdown.
Growing a small account fast: risk per trade and ruin
«Flipping» a small account means trying to multiply it quickly by risking a lot on every trade. Take a strategy with a 45% win rate and an average win 1.5 times the average loss: the expectancy is 0.45 × 1.5 − 0.55 = +0.125R per trade (R is the amount at risk). At 20 trades a month the «plan» is 2.5R: 2.5% a month at 1% risk, and 10% a month needs 4% risk.
| Risk per trade | «Plan» per month | Typical year | Chance of a 50% drawdown within a year |
|---|---|---|---|
| 1% | 2.5% | +32.5% | ≈ 0% |
| 2% | 5% | +69.1% | 0.6% |
| 4% | 10% | +147.1% | 31.1% |
| 10% | 25% | +227.6% | 99.6% |
| 20% | 50% | −67.4% | 100% |
A year is 240 trades, and risk is a share of the current capital, so it compounds. The typical year is the median: half of the accounts finish better, half worse. The drawdown is measured from the peak with the Monte Carlo model of the risk of ruin calculator; it is not a forecast.
At 4% risk the typical year brings 147%, not 214%, and almost one account in three loses half of its peak along the way. At 10% such a drawdown is close to certain, and above 17% risk the typical account shrinks even though each trade is profitable on average. That is why the baseline is 1–2% per trade, as explained in «The 1% rule: how much to risk per trade and why».
Deposits and withdrawals: why returns exclude them
You have $1,000 and make +10% in a month — $1,100. You add $1,000 — now $2,100 — and the next month brings another +5% — $2,205. «Start vs. end» says +120.5%, while you earned $205 and the rest is your own deposit.
So the return of a strategy is measured over the stretches between deposits and withdrawals, and those returns are multiplied — the time-weighted return (TWR): 1.10 × 1.05 − 1 = +15.5%. A withdrawal is not a loss either. TWR and XIRR are covered in «Portfolio return with deposits: TWR and XIRR explained».
The rule of 72
A quick estimate of the doubling time: periods to double ≈ 72 / r, where r is the return per period in percent. The exact formula is ln 2 / ln(1 + r).
| Return per period | Rule of 72 | Exact | Error |
|---|---|---|---|
| 2% | 36 | 35.0 | +2.8% |
| 5% | 14.4 | 14.2 | +1.4% |
| 10% | 7.2 | 7.3 | −1.0% |
| 20% | 3.6 | 3.8 | −5.3% |
The rule is most accurate around 8% (9 vs. 9.01), stays within 3% between 2 and 10%, and understates the time at high rates.
How Davinchu measures account returns
On the account page your deposits never pass for profit:
- «Growth» is the return over the whole history compounded by year, and «Abs. growth» is the same as a simple percentage. Deposits and withdrawals are not counted as profit. For MetaTrader 5 accounts connected with the Davinchu Trade Monitor EA and for Bybit they come from the account itself, and the base is your deposits: each year is measured against the balance at its start plus that year's deposits, a withdrawal does not reduce the base, and broker bonuses are not part of it.
- «Monthly returns» — in percent and money; the «Year summary» shows the «Annual return» (compounded from the months) and the best, worst and average month.
- «AHPR / GHPR» on the «Trades» tab — how much growth the spread of results eats (exchange futures accounts show Funding here).
- «Max drawdown» — the larger of two: from the account curve and from hourly equity snapshots, with floating losses.
- «Risk of ruin» for a 50% and a 100% drawdown on the «Risk» tab — from the expectancy and spread of your trades: bigger trades, higher estimate.
- The «Investments» section — «TWR return» and «XIRR / MWR» from hourly snapshots of the portfolio value.
The Free plan connects two accounts at no cost; where to start — on the «Davinchu for beginner traders» page.