How the time-to-target math works
Most compound-interest tools answer "what will I have after N years?" This one inverts the question: given a starting balance (PV), a monthly contribution (PMT), and a monthly rate (i = annual rate ÷ 12), it solves for the number of months n at which the balance first reaches the target (FV). Because the future-value formula can be rearranged with logarithms, no trial-and-error is needed — the answer is exact, then rounded up to the first whole month-end at or past the target.
The time-to-target solve
FV = PV(1 + i)n + PMT · [(1 + i)n − 1] ÷ i
n = ln[(FV·i + PMT) ÷ (PV·i + PMT)] ÷ ln(1 + i)
where contributions land at the end of each month (an ordinary annuity) and i is the annual return divided by 12. At a 0% return the formula degenerates to simple division,n = (FV − PV) ÷ PMT, and with no growth and no contributions the target is unreachable — the calculator says so rather than inventing a number.
Worked example
Take the default plan: a 30-year-old with $50,000 invested, adding $1,000 a month at a 7% expected return, aiming for $1,000,000:
| Step | Amount |
|---|---|
| The plan$50,000 already invested, $1,000 added at the end of every month | 7% return |
| Solve for n (months)n = ln[(FV·i + PMT) ÷ (PV·i + PMT)] ÷ ln(1 + i), with i = 7% ÷ 12 | 287 months |
| You contribute along the way$50,000 start + $1,000 × 287 months | $337,000 |
| Investment growth supplies66% of the arrival balance of $1,004,017 | $667,017 |
| = 23.9 years to $1,000,00023 yrs 11 mos — a 30-year-old arrives at age 53.9 | 23.9 yrs |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then swap in your own plan.
Why the first $100,000 is the slowest
Compounding pays in proportion to what you already have, so the early years are almost all your own deposits doing the work. Charlie Munger put it memorably at a Berkshire Hathaway meeting: getting the first $100,000 is the hardest part — do whatever it takes, he told a young shareholder, because after that the snowball rolls itself. The engine makes his point precisely. Here is the same default plan, solved for each milestone along the way:
| Milestone | Time from today | Time for this stretch |
|---|---|---|
| $100,000 | 3 yrs | 3 yrs |
| $250,000 | 9 yrs 3 mos | 6 yrs 3 mos |
| $500,000 | 15 yrs 11 mos | 6 yrs 8 mos |
| $1,000,000 | 23 yrs 11 mos | 8 yrs |
Read the third column: reaching $100,000 takes 3 yrs even though the plan starts halfway there, yet the final stretch from $500,000 to $1,000,000 — half a million dollars — takes only 8 yrs. Nothing about the plan changed; the balance simply got big enough that 7% of it outearns your deposits. This is why the standard advice is front-loaded: contributions matter most exactly when they feel least rewarding.
The inflation reality check
A million dollars 23.9 years from now is not a million of today's dollars. At 2.5% inflation, the $1,000,000 the default plan reaches in 23.9 years buys only about $550,298 in today's terms. Flip on the calculator's inflation toggle and it solves the stricter problem — a target that grows with inflation while your balance chases it: being a millionaire in today's purchasing power takes 35.3 years on the default plan, and the number you actually cross that day is $2,411,703. Neither answer is wrong; they answer different questions, and serious plans should look at both.
To see the same plan from other angles, project a balance forward with thecompound interest calculator, work out the monthly saving a specific goal requires with thesavings goal calculator, or ask when the portfolio could fund your living costs entirely with theFIRE calculator.
Frequently asked questions
How long does it take to become a millionaire?
It depends almost entirely on three numbers: what you already have, what you add each month, and the return you earn. With this calculator's default plan — $50,000 invested, $1,000 a month, and a 7% annual return — the engine solves to 23.9 years. Doubling the monthly contribution or starting with more shortens that dramatically, because time is the one input you cannot buy back. There is no typical answer; the point of the closed-form solve is that your plan has an exact one.
Why is the first $100,000 the hardest?
Because early on, compounding has almost nothing to compound. On the default plan, reaching $100,000 takes 3 yrs even though it starts halfway there, while the final stretch from $500,000 to $1,000,000 — ten times as much new money — takes 8 yrs. Charlie Munger's famous advice to a young shareholder was blunt: the first $100,000 is the hardest, do whatever it takes to get there, because after that the money starts working harder than you do. The milestone table above shows exactly that arithmetic.
Does the $1 million target account for inflation?
Not by default — the headline answer is nominal, the day your statement first prints seven figures. Turn on the inflation toggle and the engine also solves the harder problem: reaching $1,000,000 of today's purchasing power while the target itself grows with inflation. At 2.5% inflation the default plan needs 35.3 years instead of 23.9, and the number you actually cross by then is $2,411,703. Both answers are useful; just know which question you are asking.
What rate of return should I assume?
The default of 7% is a common planning figure for a diversified stock portfolio: roughly the long-run US market return after inflation, or a conservative haircut to the nominal average. Cash and bonds earn less; concentrated bets are anyone's guess. The honest approach is to run the calculator at several rates — say 5%, 7%, and 9% — and treat the spread as your uncertainty, not the midpoint as a promise. Small rate changes move the answer by years, which is itself worth seeing.
How much of the final million comes from my contributions vs growth?
On the default plan, you put in $337,000 — the $50,000 you start with plus $1,000 a month for 287 months — and investment growth supplies the remaining $667,017, about 66% of the arrival balance. That split flips over time: in the early years your deposits are nearly all of the progress, while in the final years the portfolio's own growth adds more per year than you do. The split bar in the calculator recomputes this for any plan you enter.
Disclaimer: This calculator is foreducation and illustration only. It assumes a constant return compounded monthly and steady contributions — real markets deliver returns unevenly, and sequence, taxes, and fees all change the arrival date. Results are a textbook projection, not a forecast, and nothing here is investment, financial, or tax advice.