Millionaire Calculator
How long until your savings hit one million, given your current amount, monthly contribution and annual return.
Input Data
Results
At a glance:The millionaire model finds how long a growing balance takes to hit a target. With an opening balance P, monthly contribution C and monthly rate r = annual% ÷ 100 ÷ 12, the balance after n months is P(1+r)^n + C × ((1+r)^n − 1) ÷ r; the calculator solves for n when the balance equals the target.
Formula
Monthly rate r = annual return% ÷ 100 ÷ 12.
Balance after n months = P(1+r)^n + C × ((1+r)^n − 1) ÷ r.
Years to reach = months to target ÷ 12.
$$n = \dfrac{\ln\!\left(\dfrac{T + PMT/r}{S + PMT/r}\right)}{\ln(1 + r)},\quad r = \dfrac{annual\%}{12}$$$$Contributed = S + PMT \times n$$How to Use
- Enter your current savings and monthly contribution.
- Enter the expected annual return and target amount.
- Read the years and months to reach the target.
FAQ
Is raising my monthly contribution or chasing a higher return more effective?
Both help, but raising your monthly contribution is usually the most reliable, controllable accelerator and carries no extra market risk, whereas chasing a higher return usually means taking on more risk. Over the long run, compounding gradually amplifies the effect of the return.
Is the return guaranteed?
No. The tool assumes a fixed annual return compounded monthly, but real returns fluctuate. Treat the result as planning guidance and keep a disciplined, diversified, long-term approach.
Does it account for inflation?
This calculator works in nominal terms and does not subtract inflation. One million in several decades will have lower purchasing power than today. To measure in today's money, use a 'real return' (nominal return minus inflation) as the annual return.
Why is raising the monthly contribution more reliable than chasing a higher return — how big is the difference?
Many people think 'go for a higher return' is the shortcut to wealth, but the numbers say otherwise: within your control, raising the monthly contribution is often the more reliable, lower-risk accelerator. Take the default (target HK$1m, current HK$10k, 7% return): raising the monthly contribution from HK$3,000 to HK$5,000 to HK$8,000 to HK$12,000 cuts the time from about 15.2 to 10.9 to 7.7 to 5.6 years — each step shortens the goal noticeably, entirely under your control and with no market risk. Now raising the return from 0% to 4% to 7% to 10% (at HK$5,000/month) gives 16.5, 12.6, 10.9 and 9.7 years — going from 7% to 10% saves only about 1.2 years, but those 3 extra percentage points usually demand far greater volatility and loss risk, and are 'not guaranteed'. Comparatively, lifting the monthly contribution from 5,000 to 8,000 saves over 3 years — a bigger and certain effect. Conclusion: first maximise your savings rate and monthly contribution (controllable, risk-free), then consider returns within a sensible range — that is the steady path to wealth.
What is the relationship between total contributed and the final one million — how much does compounding contribute?
The 'total contributed' is the real cash you put in (current savings + monthly contribution × months), and the gap between the HK$1m target and that amount is what compounding earned for you — the bigger the gap, the harder your money worked for you. With the default (HK$1m, current HK$10k, HK$5,000/month, 7%), it takes about 131 months (10.9 years) and total contributed ≈ HK$664,694 — so you actually put in only about HK$665k, and the remaining ≈ HK$335k (one-third of the target) came from compounding. Two patterns stand out: (1) the longer the time, the larger the compounding share — compounding is a snowball whose later growth accelerates, so slower-to-reach plans (e.g. low contributions) actually have a higher compounding share; (2) the higher the return, the lower the principal share — at 0% return you must fund the full HK$1m yourself, while higher returns shift more of the burden to compounding. This shows the power of 'start early + contribute steadily + let time work' — the earlier you start, the longer compounding has to magnify your principal.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.