The formula: working backward from your goal
The future value of annuity formula tells you what monthly deposits become. Flip it around and it tells you what monthly deposits you need:
PMT = FV x i / ((1 + i)^n - 1)
FV is your target. i is the monthly rate: your expected annual return divided by 12. n is the number of months: years times 12. The formula assumes deposits at the end of each month and a constant rate, the same assumptions behind every standard projection. Every table below was computed from this formula and rounded to the nearest dollar.
Monthly investment to reach $1 million
| Horizon | At 5% | At 7% | At 8% |
|---|---|---|---|
| 10 years | $6,439 | $5,778 | $5,466 |
| 20 years | $2,433 | $1,920 | $1,698 |
| 30 years | $1,202 | $820 | $671 |
| 40 years | $655 | $381 | $286 |
Read the table as a negotiation between time, rate, and effort. A 40-year saver at 7 percent needs $381 a month. Give the same goal to a 20-year saver and it costs $1,920 a month, five times as much, for the same million. Push the 40-year saver from 7 to 8 percent and the bill drops from $381 to $286, saving $95 a month for one extra point of return.
The short-horizon column shows how brutal a late start is. At 7 percent, $1 million in 10 years takes $5,778 a month, which is $69,336 a year in contributions alone. That is why financial planners talk about time as the most valuable asset: it is the only input that can cut the monthly bill by 80 percent.
Monthly investment for smaller targets at 7 percent
| Horizon | $100,000 target | $250,000 target | $500,000 target |
|---|---|---|---|
| 10 years | $578 | $1,444 | $2,889 |
| 20 years | $192 | $480 | $960 |
| 30 years | $82 | $205 | $410 |
These smaller targets show how reachable steady investing is on an ordinary budget. $500,000 at 7 percent over 30 years takes $410 a month, which is $4,920 a year. A $100,000 emergency-fund-scale goal over 20 years takes $192 a month. Goals scale linearly in this table: half the target is exactly half the monthly deposit.
Your existing savings count double
The tables assume you start from zero. Most people do not. Existing savings do double duty: they keep compounding on their own, and they shrink the monthly deposit you still need.
Worked example. You have $50,000 saved, you want $1 million in 30 years, and you expect 7 percent. The $50,000 compounds to 50,000 x 1.0058333^360 = about $405,825 on its own (monthly compounding of a 7 percent nominal rate). Your remaining target is 1,000,000 - 405,825 = $594,175. The monthly deposit for that remainder is 594,175 x (0.07/12) / (1.0058333^360 - 1) = about $487 a month, down from $820. The head start saves you $333 a month, nearly $120,000 over 30 years, before you lift a finger.
What the employer match does to these numbers
If your job matches retirement contributions, every dollar you put in can be worth more than a dollar toward these tables. A 50 percent match on 6 percent of salary effectively multiplies your early contributions. The tables still apply, just feed them your total monthly input, your deposit plus the match, instead of your deposit alone. That is also why capturing the full match is the first move before any of these numbers matter: it is an instant return no market can offer.
The assumptions behind every number here
These tables assume a constant rate, monthly deposits at month end, and no taxes, fees, or inflation adjustments. Real returns will differ, and a 7 percent projection does not promise 7 percent outcomes. Use the numbers to compare plans and set a contribution level, not to predict an exact balance. For education only, not financial advice.