How the result is calculated
An investment plan has three moving parts: a sum you start with, contributions you add along the way, and a return that grows whatever has built up. The calculator steps through the plan one contribution period at a time, a month or a year. In each period it adds the contribution, at the start or the end as you choose, and grows the balance by one period's return. Once a year it raises the contribution by the increase you set, which is how most people's saving behaves as their pay rises.
The return is read as an effective annual rate, the way funds and indices report performance. For a monthly plan, each month's growth is the twelfth root of a year's:
i(1 + r)1 ÷ 12 − 1
- i
- the growth applied each month
- r
- the expected annual return as a decimal
A projection decades ahead is in the money of that day, and prices will have risen in the meantime. To show what the balance would buy today, the calculator divides it by the growth in prices over the same years, and states the real return, the growth after inflation, with the exact relation rather than a subtraction:
value in today's moneyB ÷ (1 + π)t
- B
- the projected balance after t years
- π
- the expected annual inflation as a decimal
Worked example
| Item | Amount | How it is obtained |
|---|---|---|
| Growth a month, i | 0.5654% | 1.071 ÷ 12 − 1 |
| Starting sum grown | $54,274.33 | 10,000 × 1.0725 |
| Contributions grown | $391,520.94 | 300 deposits of 500 at the end of each month |
| Balance, B | $445,795.27 | 54,274.33 + 391,520.94 |
| Paid in | $160,000.00 | 10,000 + 300 × 500 |
| Price rise over 25 years | 1.8539 | 1.02525 |
| In today's money | $240,457.77 | 445,795.27 ÷ 1.8539 |
Growth contributes 285,795 of the balance, more than you paid in. In today's money the balance is still half as much again as the 160,000 contributed.
| Item | Amount | How it is obtained |
|---|---|---|
| Contribution in year 1 | $300 a month | Contribution each month |
| Contribution in year 30 | $707 a month | 300 × 1.0329 |
| Paid in | $171,271.50 | thirty years of rising contributions |
| Balance, B | $408,775.87 | at 0.4868% a month |
| In today's money | $194,880.91 | 408,775.87 ÷ 1.02530 |
With the contribution held at 300 the balance would be 292,353.89. The 3% yearly rise adds 116,422 to the end value for 63,272 more paid in.
Reading the result
The headline is the balance at the end of the plan. The control beneath it switches between the figure as it will be, in the money of that day, and the same figure in today's money; the qualifier always gives the other one, so both are in view. Total paid in is your starting sum plus every contribution; investment growth is the rest of the balance; the real return is the yearly growth you are left with after inflation.
The chart draws three lines: the balance as it will be, the balance in today's money and the cumulative amount you paid in. Where the today's-money line sits above the paid-in line, the plan has grown your buying power; where it sits close, it has merely kept pace.
What changes the result
The return and the number of years dominate. Each extra year at the end of a long plan adds more than the year before, because it compounds the whole balance, which is why starting early does more than saving more later.
Raising contributions each year is the most practical lever most people have. A modest yearly increase lifts the end value by far more than its share of the money paid in, because the larger contributions arrive while there is still time for them to grow.
Inflation changes nothing about the balance, only about what it means. At 2.5% a year, prices rise by 85% over 25 years; at 3.5% they more than double. If your goal is in today's prices, read the today's-money figure.
Timing matters at the margin: contributions at the start of each period earn one more period of growth than at the end.
What is not included
The calculator applies one return every year. Real portfolios rise and fall, and two plans with the same average return can end far apart depending on the order of good and bad years, especially near the end of a plan when the balance is largest. Tax on growth, income and withdrawals is not deducted; wrappers such as pensions and tax-free accounts change it greatly. Charges are included only if the return you enter is already after them. Withdrawals, missed contributions and lump sums added part way through are not modelled.
Using the result
Use the projection to test whether a plan is roughly the right size, in today's money, for the goal you have in mind, and run it at more than one return to see how much depends on the markets. If a goal is reachable only at an optimistic return, the safer adjustments are more years or larger contributions. For a goal at a fixed date, the savings goal calculator works backwards to the monthly sum; for retirement, the retirement and FIRE calculators turn a balance into an income.