Investment calculator

What does this investment calculator work out?

It answers two questions about a regular investing plan. The first tab, What it grows to, takes a starting amount, what you add each month or year, an assumed yearly return and a number of years, and projects the value at the end. The second tab, Amount for a target, runs the same arithmetic backward: give it a target and a date and it returns the monthly or yearly amount that gets there at your assumed return.

On the defaults, $10,000 plus $500 a month at an assumed 6% a year is projected to reach $258,791 after 20 years. Of that, $130,000 is money you paid in and $128,791 is growth, which is 49.8% of the final value. Switch to the target tab and the same start needs $480.61 a month to reach $250,000 in 20 years.

The optional setting under Raise contributions each year lifts every contribution by a percentage once a year, for example to keep pace with pay rises. It changes the answer a lot, as the section on rising contributions shows.

How do you calculate investment growth with monthly contributions?

The projection has two parts added together. The starting amount grows as a single sum: S x (1 + r)^n, where S is the start, r the assumed yearly return as a decimal and n the years. Each contribution then grows from the month it is paid until the end, and summing them gives the second part.

The one convention to know is how a yearly return becomes a monthly one. This page treats the assumed return as genuine yearly growth, so it uses the monthly rate (1 + r)^(1/12) - 1. At 6% that is 0.4868% a month, and twelve months of it compound to exactly 6.00%. The compound interest page here, set to monthly compounding, divides a quoted rate by 12 instead: 0.5% a month, which compounds to 6.168% a year. Applied to the defaults, the divide-by-12 method projects $264,122 instead of $258,791, so the two approaches part company by more than $5,000 over 20 years. Neither is wrong; they describe different things. A bank quotes a nominal rate before compounding, while the return entered here is read as what a full year delivers.

With flat monthly contributions c, the contribution part is c x ((1 + i)^(12n) - 1) / i, where i is that monthly rate. Contributions are added at the end of each month, after the month's growth. The working under the result sets out both parts with your own numbers.

How much do I need to invest each month to reach a goal?

Work out what the starting amount alone grows to, take that from the target, and divide the gap by what one unit a month grows to over the same period. Because the projection is a straight multiple of the contribution, this gives the exact amount with no trial and error.

For the default goal of $250,000 in 20 years at an assumed 6%: the $10,000 start grows to $32,071, leaving a gap of $217,929. One dollar a month for 240 months at the matching monthly rate grows to $453.44. So the amount needed is 217,929 / 453.44 = $480.61 a month. Over the 20 years you would pay in $125,347 and the plan relies on $124,653 of growth to close the rest.

If the start alone is projected to reach the target, the calculator says so and shows zero rather than a negative amount. Lengthening the time is a strong lever: five more years cuts the default from $480.61 to $306.20 a month, because both the start and each contribution have longer to compound. Raising the assumed return lowers the monthly figure too, but only on paper, which is why the range chart is there.

What do rising contributions add over 20 years?

Raising what you add by a fixed percentage each year changes the result far more than small changes to the return assumption. The formula for the contribution part becomes c x s x ((1 + r)^n - (1 + g)^n) / (r - g), where g is the yearly increase and s is what one year of monthly contributions of 1 grows to by the end of that year (12 at a 0% return, r / ((1 + r)^(1/12) - 1) otherwise).

On the defaults with a 3% yearly increase, the first year's $500 a month becomes $876.75 a month by year 20. The projected value rises from $258,791 to $319,901, an extra $61,110, while the money paid in grows from $130,000 to $171,222. On the target tab, the same 3% increase cuts the starting monthly amount for $250,000 from $480.61 to $378.57, ending at $663.83 a month in the final year.

A rising plan front-loads less money, so each dollar has less time to grow than in a flat plan of the same total. That is the trade: a lower starting amount in exchange for larger payments later.

Which return goes into the projection, and how much does it matter?

The return is an assumption you choose, and the result is only as good as that number. Real portfolios rise in some years and fall in others, and a plan's outcome also depends on the order of those years, which a single steady rate cannot show. That is why the page draws a second chart with the return moved two points either side.

Two points of return either side of 6% move the 20-year figure by about $55,000 down or $72,000 up. Whatever rate you test, use one after fund charges if you want the projection to reflect what an account could hold, and remember that a past average is not a forecast of the next 20 years.

Worked examples in pounds and dirhams

The arithmetic is the same in every currency, and switching the currency selector changes only the formatting. Nothing is converted at an exchange rate.

In the pound target example, the £5,000 start is projected to grow to £10,395 on its own, so the monthly plan only has to cover the remaining £89,605. In the dirham example, the same AED 2,000 a month held flat would reach AED 342,103, so the 5% yearly rise adds about AED 76,668 of projected value, of which AED 61,869 is extra money paid in and the rest is growth on it.

How do you calculate an investment's future value in Excel?

Excel's FV function covers a flat plan: =FV(rate, nper, pmt, pv, type). Microsoft's documentation says to keep the units of rate and nper consistent, and that cash you pay out, such as deposits to savings, is entered as a negative number. For the default example with this page's monthly rate:

=FV((1+6%)^(1/12)-1, 240, -500, -10000) returns 258,790.67, matching the calculator. Using 6%/12 as the rate instead gives 264,122.49, the divide-by-12 convention explained above.

For the target tab, Excel's PMT function solves for the payment: =PMT((1+6%)^(1/12)-1, 240, -10000, 250000) returns -480.61, the minus sign showing money paid in. Neither function handles contributions that rise each year. For that, build a yearly table in which each row's contribution is the row above times (1 + g), or use the closed-form expression from the section on rising contributions.

How does each input move the projection?

• Years. The default plan reaches $99,145 after 10 years, $258,791 after 20 and $544,691 after 30. Starting the same plan five years later, so it runs 15 years instead of 20, ends at $167,422.
• Monthly or yearly. Paying $6,000 once at the end of each year instead of $500 a month ends at $252,785, about $6,006 lower, because each month's money waits longer before it starts growing.
• Starting amount. On its own the $10,000 grows to $32,071 in 20 years at 6%. Every extra $1,000 at the start adds about $3,207 at the end.
• Assumed return. The biggest swing of all, as the table above shows, and the one you control least.
• Yearly increase. A 3% rise adds $61,110 to the 20-year default, mostly from the extra money paid in during later years.

What this calculator leaves out: tax, fees and inflation

The projection is pre-tax and pre-fee. How investment growth is taxed depends on where you live and the type of account you hold, and tax-advantaged accounts come with their own yearly limits and rules that change from time to time. This page applies none of that, so treat the result as a gross figure in any of the 24 currencies. For a UK wrapper, the stocks and shares ISA calculator works through the allowance.

Fund charges are not deducted either. To see what a yearly fee takes out of the same plan, use the fund fee calculator, or simply lower the assumed return by the fee. And the result is in future money: to restate it in today's buying power, run the figure through the real return calculator, or enter an assumed return that is already after inflation.

Finally, there are no withdrawals, no missed months and no market falls in the middle. A real plan will meet all three.

Common mistakes and a short glossary

• Reading the projection as a forecast. It is what a constant rate would produce; no market delivers one.
• Mixing a savings rate with an investment return. If you are copying a bank's quoted rate, the compound interest calculator handles its compounding frequency directly.
• Forgetting the start in a target plan. A large starting sum can cover much of a long-dated target on its own.
• Ignoring fees and tax. A one-point annual charge on the default plan is roughly the gap between the 6% and 5% projections.

Contribution: money added to the investment at regular intervals. Assumed return: the yearly growth rate you enter for the projection. Projected value: the balance a constant assumed return would produce. Paid in: the starting amount plus every contribution. Growth: the projected value minus what was paid in. Escalation: raising the contribution by a set percentage each year.

Frequently asked questions

Courses for the investing behind the projection

Sources and review