Investment Calculator

Balance grows month by month: B ← B × (1 + r ÷ 12) + C, repeated 12 × t times

B

The running balance, starting at the amount you put in on day one

C

The contribution added at the end of every month

r

The expected annual return, written as a decimal

t

The number of whole years the account is left alone

ΣC

Everything you paid in: the opening amount plus every monthly contribution

Use it for any plan where money goes in on a schedule — a retirement account, a monthly savings standing order, a child's savings plan, a regular investment into a fund. The result is most useful read as a comparison rather than as a forecast: change the years and watch what happens to the earnings, and you will find that the last few years of a long run add more than the first several. On the defaults, twenty years of contributions produce 143,502.07 of earnings; the same monthly amount over ten years produces 28,552.07. That is not a twofold difference for a twofold term, and closing the gap is the entire argument for starting early. Equally worth doing is setting the return to zero and reading the answer, which tells you what the habit alone is worth with no growth at all.

1. 1,000 to start plus 500 a month at 7% for twenty years

   1. Monthly rate: 7 ÷ 100 ÷ 12 = 0.00583333
   2. Periods: 12 × 20 = 240 months
   3. Contributions: 1,000 + (500 × 240) = 121,000.00
   4. Balance: run the recurrence 240 times — each month the balance grows by 0.583333% and then 500 is added — which gives 264,502.07
   5. Earnings: 264,502.07 − 121,000.00 = 143,502.07

   This is the page's default. The thing to notice is which of the last two numbers is bigger: the account earned 143,502.07 while you put in 121,000.00. Money earned more than money saved, and that only happens because the earliest contributions had twenty years to work.

2. Nothing to start, 500 a month at 7% for thirty years

   1. Monthly rate: 7 ÷ 100 ÷ 12 = 0.00583333
   2. Periods: 12 × 30 = 360 months
   3. Contributions: 500 × 360 = 180,000.00
   4. Balance: 609,985.50 after 360 monthly steps
   5. Earnings: 609,985.50 − 180,000.00 = 429,985.50

   Compare this with the default: the monthly amount is identical and only the term changes, from twenty years to thirty. Contributions rise by half, from 121,000 to 180,000, while the balance rises by 2.3 times. The extra ten years land on the steep part of the curve, and that is where nearly all of the difference is made.

3. 1,000 to start, nothing added, at 7% for twenty years

   1. Monthly rate: 7 ÷ 100 ÷ 12 = 0.00583333
   2. Periods: 240
   3. Balance: 1,000 × 1.00583333^240 = 4,038.74
   4. Contributions: 1,000.00, the opening amount alone
   5. Earnings: 4,038.74 − 1,000.00 = 3,038.74

   Setting the monthly contribution to zero reduces this page to plain compound growth, which is a useful sanity check on the recurrence: 1,000 at 7% compounded monthly for twenty years is 4,038.74, exactly what the compound interest page returns for the same inputs. Read it against the default too — 500 a month turns 1,000 into 264,502.07, and doing nothing turns it into 4,038.74.

The page shows one smooth path and a real portfolio is not smooth. It applies the same annual return to every one of the 240 or 360 months, which no market does; a sequence of returns with the same average but a bad decade in the middle will not land on the same balance, and the order matters more than the average. The rate is an input you supply and cannot be verified, so a plan built on 7% is a plan built on an assumption that may be wrong by several points in either direction. Two structural choices are worth stating plainly because neither is visible on the page. First, contributions are credited at the end of each month, following the convention in United States consumer credit mathematics, so paying in at the start of the month would earn slightly more than shown here. Second, compounding is fixed to monthly and the page offers no frequency field at all: contributions arrive monthly, so the account compounds monthly, and a control letting you set quarterly compounding against monthly deposits would describe something with no single meaning. Fees are not deducted and they matter over thirty years — a 0.5% annual charge would remove tens of thousands from the figure above. Tax is ignored, and it applies to a taxable account as the growth arises. Inflation is ignored, so the balance is nominal. Contributions cannot rise over time, cannot be paused, and cannot be withdrawn, and nothing here models an employer match or a contribution limit. Finally, the amounts carry no currency symbol.

How do I work out what regular monthly contributions will grow to?

Take the monthly rate, which is the annual return divided by twelve, and step through the months one at a time: each month the balance grows by that rate and then the contribution is added. 1,000 to start with 500 a month at 7% for twenty years means 240 steps at 0.583333% each, which lands on 264,502.07. The total paid in is 1,000 plus 500 times 240, which is 121,000.00, and the difference of 143,502.07 is what the account earned.

Why are the earnings larger than the money I put in?

Because the earliest contributions had twenty years to compound before you finished. On the default example the balance is 264,502.07 against contributions of 121,000.00, so earnings of 143,502.07 exceed everything you paid in. That is not a trick of the arithmetic — it is what happens when a contribution is left alone long enough, and it is why the years matter more than the amount once you are saving over decades.

Does it matter whether I contribute at the start or the end of the month?

It matters a little. This page credits contributions at the end of each month, following the convention used in United States consumer credit mathematics, so the money added in a given month has not earned anything during that month. Paying in at the start would earn one extra month of return on each contribution, which on the default example is worth roughly a few hundred over twenty years — real but small next to the difference the number of years makes.

What annual return should I assume?

The one you can justify, and you should test the plan at more than one. Long-run equity returns have historically been in the high single digits before inflation and fees, government bonds well below that, and cash lower still. Because the rate compounds over every month of the term, small differences in the assumption become large differences in the balance: 7% over twenty years on the default inputs gives 264,502.07, while 5% gives 208,229.47.

Why is there no compounding frequency setting?

Because the contributions arrive monthly, so the account compounds monthly and there is nothing left to choose. Offering a frequency control here would allow a state with no single meaning — quarterly compounding against monthly deposits does not describe any account. If you want to see what a different frequency is worth on a single lump sum, the compound interest page has that field; here the monthly rhythm is fixed by the monthly contribution.

Is the final balance what I will actually end up with?

No, it is a projection from the return you typed in. It assumes the same annual return every month for the whole term, which no market delivers, and it assumes the order of the good and bad years does not matter, which it does. Fees, tax and inflation are all absent, and each of them reduces the figure — a 0.5% annual fee alone would remove tens of thousands over thirty years. Treat the balance as the answer to what if rather than as a forecast.

• Compound Interest Calculator — the single-deposit case this page reduces to when the monthly amount is zero — U.S. Securities and Exchange Commission (Investor.gov)
• Savings Goal Calculator — the same contribution stream read backwards, from a target balance — U.S. Securities and Exchange Commission (Investor.gov)
• 12 CFR Part 1026, Appendix J — the end-of-period contribution convention used here — Electronic Code of Federal Regulations (United States)