Math for MoneyHow the monthly amount is calculated
The calculation has two parts. First, your current savings are grown at the rate you entered until the deadline. Whatever is still missing after that is the gap your monthly contributions have to fill. Second, the gap is divided by the amount that $1 saved every month would grow to over the same period.
Gap = Goal − Current savings × (1 + i)n
Monthly saving = Gap × i ÷ [(1 + i)n − 1]
Here n is the number of months and i is the monthly rate, which depends on the compounding option:
- Annually: i = (1 + annual rate)1/12 − 1, so that a full year of growth equals the annual rate exactly.
- Monthly: i = annual rate ÷ 12.
These formulas assume you contribute at the end of each month. If you contribute at the beginning of each month, every contribution earns one extra month of return, so the result is divided by (1 + i). If the rate is 0%, there is no growth and the monthly saving is simply (Goal − Current savings) ÷ n.
Worked example
Suppose you want $100,000 in 10 years, you already have $10,000, and you assume 6% a year compounded annually, with contributions at the end of each month.
- Monthly rate: i = 1.061/12 − 1 = 0.00486755, or about 0.4868% a month. Number of months: n = 10 × 12 = 120.
- Growth over the whole period: (1 + i)n = 1.00486755120 = 1.790848.
- Your current savings grow to 10,000 × 1.790848 = $17,908.48.
- The gap left to fill is 100,000 − 17,908.48 = $82,091.52.
- $1 saved every month grows to (1.790848 − 1) ÷ 0.00486755 = 162.473 dollars.
- Monthly saving: 82,091.52 ÷ 162.473 = $505.26.
Over the 10 years you would put in $70,631 in total, including the $10,000 you started with, and interest would supply the other $29,369. Contributing at the beginning of each month instead lowers the monthly amount to $502.81. At a 0% return it would be $750.00. The steps show rounded figures; the calculator uses full precision.
How time and rate change the answer
The table shows the monthly saving needed to reach $100,000 starting from $0, for different deadlines and rates of return. The rates are examples to show the effect, not forecasts. For a different goal, scale the numbers in proportion: half the goal needs half the monthly amount.
| Time | At 0% | At 3% | At 5% | At 7% |
|---|---|---|---|---|
| 5 years | $1,667 | $1,548 | $1,475 | $1,405 |
| 10 years | $833 | $717 | $648 | $585 |
| 15 years | $556 | $442 | $378 | $321 |
| 20 years | $417 | $306 | $246 | $197 |
| 25 years | $333 | $225 | $171 | $128 |
| 30 years | $278 | $173 | $123 | $86 |
Two things stand out. Doubling the time more than halves the monthly amount whenever the rate is above zero, because the early contributions have longer to earn interest. And the rate matters far more over long periods than short ones: at 7%, your own contributions still make up about 84% of the goal over 5 years, but only about 31% over 30 years.
What this calculator does not include
- Changing returns. The same rate is applied every month. Real investment returns vary and can be negative.
- Inflation. The goal is a fixed dollar amount; it is not adjusted for rising prices.
- Taxes and fees. Interest and investment gains may be taxed, and funds charge fees. Both reduce the rate you actually keep.
- Changing contributions. The monthly amount stays the same for the whole period. If you plan to raise it over time, you can start lower than the figure shown.
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Frequently asked questions
What rate of return should I enter?
Use a rate that matches where the money will actually be kept. For a savings account or certificate of deposit, enter the APY the bank quotes you. For investments there is no single right number, and the shorter your deadline, the more a bad year can hurt, so it is sensible to run a cautious rate as well as an optimistic one and plan around the cautious result. Entering 0% shows what you need if you count on no growth at all.
Will I definitely reach my goal if I save this amount?
Only if your money earns exactly the rate you entered, every month, for the whole period. A fixed-rate account such as a certificate of deposit can come close to that. Investments do not: returns change from year to year and some years are negative. The result also ignores taxes on interest and investment fees. Treat the monthly amount as a starting plan and re-run the calculation with your actual balance once a year.
Does the calculator account for inflation?
No. The goal is treated as a fixed dollar amount. If you are saving for something whose price will rise over time, such as a home down payment many years away, either enter a larger goal that reflects the future price, or enter a rate of return with your expected inflation rate subtracted from it. The second approach is an approximation, and it assumes you also raise your monthly saving in line with inflation each year.
What if the monthly amount is more than I can afford?
There are only four inputs you can change: give yourself more time, lower the goal, start with a larger lump sum, or earn a higher rate. Time is usually the most powerful and the most realistic of the four. The comparison table under the result shows how much the monthly amount drops if you take 5 years longer. A higher rate helps on paper, but chasing it means taking more risk.
Why does the calculator say I need to save $0?
Because the current savings you entered would grow past your goal by the deadline at the rate you entered, without any further contributions. If the rate is uncertain, try a lower one to see how much of a cushion you have.
Should I choose annual or monthly compounding?
If your rate is an APY or an average annual return, choose annual: that figure already includes the effect of compounding within the year. If your rate is a nominal rate or APR that compounds monthly, choose monthly: the monthly rate is then the annual rate divided by 12, which grows slightly faster over a year, so the required monthly saving is slightly lower.