What This Calculator Solves
Every investment question involves five quantities: the starting amount, the regular contribution, the return rate, the time horizon, and the ending balance. Know any four and the fifth is determined. This calculator solves for whichever one you select, which makes it useful for the questions people actually ask — not just "what will I have?" but "how much do I need to save?", "what return do I need?" and "how long will this take?".
The Future Value Formula
FV = P(1 + i)n + PMT × ((1 + i)n − 1) ÷ i
The first term is growth of the starting amount; the second is the future value of the stream of contributions. P is the starting amount, PMT the contribution per period, i the rate per period and n the number of periods. If contributions are made at the beginning of each period rather than the end, the second term is multiplied by (1 + i).
Solving for FV is direct. Solving for the rate or the number of years has no closed form when contributions are involved, so the calculator finds those numerically by bisection — narrowing the answer until it converges.
What $500 a Month Becomes
Starting from zero, contributing $500 monthly:
| Years | at 4% | at 6% | at 8% | at 10% |
|---|---|---|---|---|
| 10 | $73,348 | $81,237 | $90,062 | $99,932 |
| 20 | $181,921 | $226,719 | $284,500 | $359,130 |
| 30 | $342,635 | $487,256 | $704,275 | $1,031,422 |
| 40 | $580,532 | $953,839 | $1,610,540 | $2,775,174 |
Over 40 years at 8%, $240,000 of contributions becomes roughly $1.75 million. Over 10 years, $60,000 becomes about $91,000. The difference is not the contribution — it is the time available for returns to compound on returns.
The Cost of Waiting
$500 a month at 8%, invested until age 65:
| Start at age | Years invested | Balance at 65 |
|---|---|---|
| 25 | 40 | $1,610,540 |
| 30 | 35 | $1,071,284 |
| 35 | 30 | $704,275 |
| 40 | 25 | $454,495 |
| 45 | 20 | $284,500 |
| 50 | 15 | $168,803 |
Starting at 25 rather than 35 costs $60,000 in contributions but gains well over $1 million at retirement. This is the single most consequential table on the page, and the reason "start early" is the one piece of investing advice on which everyone agrees.
What Return Rate Should You Assume?
| Asset class | Long-run nominal return | After ~3% inflation | Volatility |
|---|---|---|---|
| Cash / savings | 2–4% | −1 to +1% | None |
| Government bonds | 4–5% | 1–2% | Low |
| Corporate bonds | 5–6% | 2–3% | Low to moderate |
| U.S. large-cap stocks | ~10% | ~7% | High |
| Small-cap / emerging markets | 10–12% | 7–9% | Very high |
| Real estate (REITs) | 8–10% | 5–7% | High |
These are long-run averages across many decades. No investment delivers a constant rate: the S&P 500 has averaged roughly 10% while individual years have ranged from −37% to +38%, and it has had stretches of more than a decade with no real gain. A calculator that assumes a fixed rate illustrates the mechanism, not the path.
The Two Enemies: Inflation and Fees
Inflation means the ending balance buys less than the same number of dollars today. At 3% inflation, $1,000,000 in 30 years has the purchasing power of about $412,000 now. The practical response is to plan in real terms — use a return of roughly 7% rather than 10% for stocks, and treat the answer as today's money.
Fees compound against you exactly as returns compound for you. On a $500 monthly contribution over 40 years at 8%:
| Annual fee | Effective return | Final balance | Cost of the fee |
|---|---|---|---|
| 0.05% | 7.95% | $1,728,000 | — |
| 0.50% | 7.50% | $1,545,000 | $183,000 |
| 1.00% | 7.00% | $1,380,000 | $348,000 |
| 2.00% | 6.00% | $1,100,000 | $628,000 |
A one percentage point difference in fees costs a fifth of the final balance. This is why expense ratios matter far more than they appear.
Order of Operations for Investing
- Contribute enough to a workplace retirement plan to capture the full employer match — an immediate 50–100% return.
- Pay off high-interest debt. Eliminating 20% credit card interest is a guaranteed 20% return.
- Build an emergency fund of three to six months of expenses in cash.
- Maximise tax-advantaged accounts — HSA, IRA, then the rest of the 401(k).
- Invest in a taxable brokerage account beyond that.
Frequently Asked Questions
Is a lump sum better than spreading it out?
Historically yes, roughly two-thirds of the time, because markets rise more often than they fall and time in the market is the dominant factor. Spreading it out reduces the risk of investing everything just before a decline, which is a behavioural benefit rather than a mathematical one.
Should I use nominal or real returns?
Use real returns — nominal minus inflation — if you want the answer in today's purchasing power. Use nominal if you are matching a future dollar figure such as a loan balance.
What return rate is safe to assume for planning?
Most planners use 6–7% nominal for a diversified stock-heavy portfolio, deliberately below the historical average, so that a shortfall is less likely than an overshoot.
Why does the calculator sometimes fail to solve for a rate?
Because no rate satisfies the inputs. If the target is below the starting amount, or so high that no plausible return reaches it, there is nothing to solve for.