10,000 Compound Interest Scenarios: When Time Beats Rate (And When It Doesn't)

We ran 10,000 deterministic Monte Carlo simulations of a 30-year compound interest portfolio to answer four questions practitioners argue about constantly. All inputs, seed, and methodology are below — reproduce any number on this page yourself.

Finding 1: Contributions out-earn starting balance in 89.8% of 30-year scenarios

We tracked two separate buckets inside each portfolio — final value attributable to the starting balance vs final value attributable to ongoing monthly contributions. Across 10,000 scenarios, the contribution bucket ended larger than the starting-balance bucket in 89.8% of cases.

The takeaway is unintuitive: with a typical $100–$2,500/month contribution and a 30-year horizon, the consistency of contributions usually does more heavy lifting than the initial deposit. The "starting late" objection assumes the starting balance carries the portfolio — the data says otherwise once your horizon is long.

Finding 2: Annual interest beats annual contributions at year 8 (median)

This is the crossover point investors are looking for: the year in which one year's interest accrual exceeds one year's added contributions. Across all scenarios where it happens at all (97%+), the median crossover is year 8. 374 of 10,000 scenarios never cross over in 30 years — exclusively low-rate, low-starting-balance, high-contribution combinations.

Practical implication: if you're more than ~8 years into investing and your interest still isn't outpacing what you put in, your portfolio is in the bottom tail of outcomes — usually because of fees, low rate, or a recent restart.

Finding 3: Doubling time gives 812% more — doubling rate gives 350%

Held against a base case ($500/mo, 7%, 30 years → $609,985), here's what doubling each lever does:

Time wins by an enormous margin — but only because doubling time is mathematically more aggressive than doubling rate. The honest framing: a 7% return for 60 years is fictional for an investor with a working career, so the "time" lever has a hard cap that the "rate" and "contribution" levers don't.

Finding 4: Outcome spread is dominated by rate, not by starting balance

The 80th-to-20th-percentile spread in final values is $4,718,522. We re-ran the same simulation holding rate fixed at the mean (7%): the spread collapsed to roughly a quarter of that. Holding starting balance fixed barely moved the spread. Conclusion: rate uncertainty is the dominant driver of long-horizon outcome variance, not how much you start with.

Sample scenarios (evenly spaced across the distribution)

Methodology

• 10,000 scenarios, each simulated for 30 years with monthly compounding.
• Starting balance: uniform $0–$100,000.
• Monthly contribution: uniform $100–$2,500.
• Annual rate: normal distribution, mean 7%, std dev 3%, clipped to [2%, 14%]. Generated via Box-Muller.
• PRNG: Mulberry32, seed 20260523. Numbers are reproducible build-to-build.
• Compounding: contribution added at end of each month; interest applied on prior month's balance.
• Bucket tracking: we maintain two parallel balances inside each scenario — one for the starting deposit, one for ongoing contributions — to attribute final value to each source.
• Excluded: taxes, fees, inflation, withdrawal phases, sequence-of-returns risk. This is gross nominal compounding only.

Limitations

• Annual rate is sampled once per scenario — no path dependence, no sequence-of-returns risk.
• Inflation is not modeled. All numbers are nominal USD.
• The normal-distribution rate is a simplification. Real equity returns are fatter-tailed (skewed, leptokurtic).
• Monthly contributions are flat across the 30-year horizon — no income growth, no employer match modeling.