Compound Interest Calculator

What compounding does, and why the mental shortcut fails

Compound growth means the return is paid on the balance rather than on the original amount, so every period’s gain joins the pile and earns a return of its own. Over a few years that is a rounding difference. Over a few decades it is most of the result.

The usual mental shortcut is to multiply the annual return by the number of years. That is simple interest, and it quietly assumes every gain is taken out and spent. Put 10,000 in at 6% a year and simple interest says 28,000 after thirty years; compounded annually it is about 57,400. The shortcut is not slightly wrong, it is wrong by more than the starting amount.

Monthly contributions cannot be multiplied through either, and this is the part most people get wrong when they try it on paper. Each deposit grows for a different length of time: the first one for the whole period, the last one for a single month. The only correct way is to work out the growth of each deposit separately and add them up, which is what the annuity term on the right of the formula below does in one step.

The formula

FV = P × (1 + r/n)^(nt) + C × [((1 + r/n)^(nt) − 1) / (r/n)]
P = starting amount, C = contribution per period, r = annual return, n = compounding periods per year, t = years

Everything on this page comes from those two terms. The return and the inflation rate are assumptions that you type in, and the output is only as good as they are.

Run the sample values loaded on the page, 10,000 to start and 500 a month at an assumed 7% for 20 years. You put in 130,000 and finish with about 300,851, so about 170,851 of the result came from growth rather than from you. On those same inputs the interest only passes the amount contributed during year 17, which is the honest shape of compounding: nothing much happens for a long time, and then the balance starts doing more work than the monthly deposit does.

Which mode, and what each box is asking

There are two modes at the top. Use Forward when you know what you can put in every month and want to see where it lands. Use Work back from a goal when you know the number you need and want the monthly figure that gets you there.

• Starting amount: the money going in today. Enter 0 if you are starting from nothing.
• Monthly contribution: what you will add every month from here. This is the box worth agonizing over, because it is the only input you actually control.
• Annual return: your assumption, not a quote. Run it once at the figure you hope for and once two points lower.
• Compounding frequency: monthly, quarterly or annually. It also decides when your deposits are credited, so annual compounding settles a whole year of deposits at the end of that year.
• Inflation per year: discounts the final balance back to what it would buy at today’s prices. Set it to 0 and that card disappears.
• Amount you already have (goal mode): money set aside for this goal already. It is grown on its own and taken off the target before the monthly figure is worked out.
• Contribution timing (goal mode): money paid in at the start of the month earns one extra month of growth, so the required amount comes out slightly lower than for end of month.

Amounts are plain numbers with thousands separators and no currency symbol. Read them in dollars, pounds, euros or anything else; the arithmetic does not change.

How to project twenty years of monthly investing

1. Stay on Forward. The numbers on screen are a sample so the page has something to draw; replace all four.
2. Put what you are investing today in the starting amount. The line under the box repeats it with separators, which is how you catch a missing zero.
3. Enter the monthly contribution you can genuinely sustain, not the one you would like to sustain. A figure you abandon in year three makes the whole projection fiction.
4. Enter an annual return you are prepared to defend, then lower it by two points and run it again. The gap between the two results is more useful than either number alone.
5. Read the three cards: final balance, total contributed, total interest. The third is what compounding added; the second is what you did.
6. On the growth chart, find the year where the interest band gets thicker than the contributions band. That crossover is the point where the balance is doing more work than you are.
7. Fill in an inflation assumption and a second card appears showing the same balance in today’s money. A million thirty years out is not a million now.
8. Scroll the year-by-year table for any single year. Every row shows what you had put in, what the interest had added, and the year-end balance.
9. To compare two sets of assumptions, use the Recent 5 list under the results. It keeps your last few inputs, and one tap restores a set.

How to work back from a target to a monthly amount

1. Switch to Work back from a goal. The panel changes and asks five things.
2. Enter the target, then how long you have: either a number of years, or switch to Target date and pick the day you need the money. With a date, the calculator counts the whole months from today and plans one deposit a month.
3. Enter an assumed annual return. It is still an assumption here, and it moves the answer a lot, so try a cautious one as well.
4. Put anything you have already set aside for this goal into amount you already have. It compounds on its own to the end date, and only the shortfall is spread across the monthly deposits. Leave it at 0 if there is nothing yet.
5. Pick start or end of month. End of month is the conservative choice and returns the slightly higher monthly figure.
6. The large number is the monthly amount, rounded up to a whole unit, so an automatic transfer at or above it is safe.
7. If the answer is out of reach, lengthen the timescale or lower the target and run it again. Those two levers are real; raising the assumed return only changes the spreadsheet.

The rule of 72

Divide 72 by the annual return and you get a rough doubling time: 6% doubles in about 12 years, 8% in about 9, 12% in about 6. The figure shown under the results uses exactly that, which is why it is labeled as an approximation.

It is accurate enough for mental arithmetic in the middle single digits and drifts at the extremes. The exact doubling time at 8% is 9.006 years, so the rule is off by less than a week; at 1% the true answer is 69.7 years against the rule’s 72. Use it to sanity check an order of magnitude, never as the number you plan around.

The same sum in a spreadsheet, and why quoted rates differ

If you want to reproduce or extend this in a spreadsheet, Excel, Google Sheets and LibreOffice Calc all take the same two functions. Rates are per period, so a 7% annual return compounded monthly is entered as 7%/12 with 20*12 periods:

=FV(7%/12, 20*12, -500, -10000, 0)
=PMT(5%/12, 20*12, 0, 1000000, 0)

• Signs are a convention, not a bug: money you pay in is negative and money that comes back is positive, which is why the contribution and the starting amount are entered as negatives above. Mixing the signs is the usual reason a spreadsheet answer looks absurd.
• The last argument is the timing: 0 means the end of each period, 1 means the start. It is the same switch as the contribution timing in this page’s goal mode, and leaving it out defaults to 0.
• Nominal is not effective: 7% a year compounded monthly is an effective 7.23%, because (1 + 0.07/12)^12 − 1 works out at 0.0723. A product advertising an annual equivalent rate has already done that conversion for you; one quoting a nominal rate has not.
• Other calculators will not match to the unit: some credit deposits at the start of the period, some compound daily, some round each month. A few percent of difference between two honest calculators over twenty years is normal. If two results differ by a lot, the compounding basis or the deposit timing is almost always why.

If a bank or broker calculator disagrees with this one and you want to know why, set the monthly contribution to 0 on both and compare again. With the deposits out of the way, any remaining gap is the compounding basis alone. Put the contribution back and a new gap appears only if the two tools credit deposits at different points in the period. That takes about a minute and usually explains the whole difference.

What this number is not

• The return is your assumption, not a rate this page looked up or endorses. Markets do not hand out the same figure every year, and a smooth curve drawn from one number will not match a real sequence of good and bad years even if the average matches.
• Tax, fees and currency are all excluded. So is any income you take out and spend rather than reinvest. How investment income and gains are taxed depends on where you live and on the account the money sits in.
• The compounding choice moves the result: with annual compounding, a year of deposits is settled at the end of that year, so the same inputs return less than with monthly compounding.
• The goal mode is simple: monthly compounding, a fixed return for the whole period, and the same return applied to any amount you already have.
• The rule of 72 is an approximation for doubling time. It is a sanity check, not a result.

This is a calculator, not investment advice, and it does not recommend any product, fund or strategy. Whether to invest, in what, and how much, is yours to judge against your own circumstances and tolerance for loss, and it is worth talking to a qualified advisor in your country if the decision is a large one.

Over long horizons, adding years usually moves the final balance more than adding a point or two to the assumed return. Try both on the tool and see. Only one of them is under your control.