Compound Growth Calculator

About this tool

A mathematical and educational calculator for modelling compound growth, goal-based planning, withdrawal sustainability, and position sizing with the Kelly Criterion. Computations run server-side and visualise a range of outcomes rather than a single point estimate.

Educational tool only — not financial advice. Do your own research before making any decision.

What the calculator covers

• Growth Calculator — project compounding over time given a starting amount, periodic contributions, expected annual yield, annual fee (TER), per-contribution transaction cost, and inflation. Toggle between nominal and real values; compare two scenarios side by side.
• Goal Planner — solve for either the periodic contribution needed to reach a target (fixed expected return) or the return required (fixed contribution). Includes a sensitivity matrix across time horizon and yield.
• Simulations — rolling-window historical backtests and Monte Carlo projections using the historical mean and standard deviation of indices such as S&P 500, Nasdaq 100, MSCI World, and the Swiss Performance Index. Fan charts show median, interquartile, and tail bands.
• Withdrawal Planner — model fixed-rate withdrawals against a portfolio, the 4% rule, and the sustainable real-return-based withdrawal rate, with optional inflation adjustment.
• Withdrawal Simulations — stress-test a withdrawal plan against sequence-of-returns risk using Monte Carlo and historical backtests, with success rates reported at 10-, 20- and 30-year horizons and over the full simulated period.
• Kelly Allocation — compute the optimal fraction of capital to allocate to a risky asset using the continuous Kelly formula f* = (mu - r) / sigma squared, with fractional-Kelly variants and an efficiency curve.
• Position Sizing — binary-outcome Kelly: f* = (p * b - q) / b, with edge, ruin, and drawdown analysis across position sizes.
• Bond Return — compute exact yield to maturity from coupon, current price, par, and maturity, with annual or semi-annual coupon frequencies and a price-yield sensitivity table.

The compound growth formula

Future value with regular contributions is given by:

FV = PV × (1 + r)ⁿ + PMT × [ ((1 + r)ⁿ - 1) / r ]

where FV is the future value, PV is the present (starting) value, r is the periodic rate, n is the number of periods, and PMT is the periodic contribution. Fees (TER) and transaction costs reduce the effective contribution and the compounding rate.

Why simulations matter

A single “expected return” figure hides the underlying distribution of outcomes. The simulation tabs run rolling-window historical backtests (multiple starting points across the index history) and Monte Carlo projections (1,000 scenarios generated from the historical mean and standard deviation under a geometric Brownian motion assumption). The fan charts show the 10th, 25th, 50th, 75th, and 90th percentile paths, which makes the range of plausible outcomes explicit.

For withdrawal modelling, sequence-of-returns risk dominates: two paths with the same average return can produce very different outcomes depending on when the bad years occur. The withdrawal stress test reports the success rate (fraction of scenarios in which capital is not depleted) at multiple horizons.

Kelly Criterion in brief

The Kelly Criterion sizes positions to maximise the long-run geometric growth rate. For a risky asset with expected return mu, risk-free rate r, and variance sigma squared, the optimal fraction is f* = (mu - r) / sigma squared. For binary outcomes with win probability p, loss probability q = 1 - p, and win/loss ratio b, the optimal fraction is f* = (p × b - q) / b. Allocating above Kelly reduces growth and increases volatility (the worst-of-both-worlds region); fractional Kelly (typically half-Kelly) trades a small loss in expected growth for a large reduction in drawdowns and is the more practical default.

Disclaimer

This calculator is an educational and mathematical tool only. It is not financial advice, not a recommendation, and not a solicitation. Results are illustrative and depend on the assumptions provided. Past performance does not guarantee future results. Do your own research and consult an independent qualified professional before making any decision.