Nine investing calculations worth doing yourself

Most investing advice is delivered as adjectives. Fees are "low", a dividend is "safe", a portfolio is "diversified". The arithmetic behind those words is usually simple, and running it yourself changes what you do more reliably than reading another opinion. Below are nine calculations worth doing, each with the answer our own free calculators produce on a realistic set of inputs, so you can see what the number looks like before you open anything.

The nine, at a glance

Every figure in this table comes from the linked calculator on its default inputs. Nothing here is rounded for effect.

Four calculations about reaching retirement

These are the same journey seen from four angles, and they are worth doing in order rather than picking the one that sounds most relevant.

Coast FIRE is the earliest milestone and the one most people underestimate. It is the point where what you have already saved will compound to your target on its own, with no further contributions. The formula is a single division: your target divided by growth over the years remaining. On a $1.5 million target at a 7% real return, a forty-year-old needs $276,400 to coast to 65. Reach that and saving becomes optional, which usually arrives more than a decade before independence does. The Coast FIRE calculator shows the crossover point on your own numbers.

Barista FIRE asks the same question assuming you keep earning something. Subtract your part-time income from your annual spending and apply a withdrawal rate to what is left. Spending $50,000 with $20,000 of part-time income leaves a $30,000 gap, needing $750,000 rather than the $1.25 million full independence would take. The exchange rate is exactly linear and it is striking: at 4%, every $10,000 of annual income removes $250,000 from the target.

The safe withdrawal rate question comes next, and the honest answer is not 4%. On a $1 million portfolio earning 4% after inflation over 30 years, the highest rate that survives is 5.5%. Stretch the horizon to 40 years and lower the return to 3%, which is what an early retirement actually looks like, and the ceiling falls to 4.2%. The famous rule still passes, but the margin has nearly gone.

Sequence of returns risk is the one that undoes the other three, and it is the reason none of them should be trusted alone. Take an identical set of annual returns and reverse the order. Same average, same numbers, same withdrawals. On a $1 million portfolio drawing $40,000 a year, the difference between the good years arriving first and arriving last is $1.87 million. Nothing else on this page produces a gap that large from an input you cannot control.

Five calculations about growing and keeping it

Compound interest is the baseline everything else is measured against. Five thousand dollars plus $300 a month for twenty-five years at 7% becomes $271,649, of which $95,000 is money you put in. Seeing the split between contributions and growth is usually more persuasive than the total.

Dividend reinvestment adds a second compounding on top. Ten thousand dollars at a 3% yield, with the dividend growing 6% a year and the price 5%, finishes twenty years later at $49,154 with the payments reinvested against $37,569 without. The decomposition is the interesting part: annual income grows 5.9 times, which is the dividend per share growing 3.2 times multiplied by the share count growing 1.85 times. The company did roughly half the work and reinvestment did the rest. If you are choosing what to hold, our guide to the best dividend growth stocks ranks 25 of them, and how to tell if a dividend is safe covers the checks worth doing first.

The expense ratio calculation is the one that changes behaviour most often. A 1% annual fee on $10,000 plus $500 a month over thirty years takes $132,555, which is 19% of the balance you would otherwise have finished with. The reason a 1% fee costs a fifth of the pot rather than a fiftieth is that it is charged every year on a growing balance, and every dollar it takes would have compounded for the rest of your investing life.

Real returnis the sanity check on all of the above. An 8% nominal return, less a 0.5% fee, less 15% tax, against 3% inflation, leaves 3.3%. Most retirement arithmetic goes wrong at exactly this point, by compounding a nominal return against a target expressed in today's money.

Lump sum versus dollar-cost averaging is the smallest number here and the most argued about. Sixty thousand dollars invested at once beats the same amount spread over twelve months by $1,160 in a market rising steadily at 7%, with the uninvested cash earning 3%. Investing immediately usually wins because markets rise more often than they fall. Spreading it out is a decision about how you would feel if it fell, which is a legitimate reason that the arithmetic cannot price.

What all nine assume

None of them model tax, with the partial exception of the real return calculator. None of them model a market that moves in anything other than a straight line, with the deliberate exception of the sequence of returns tool, which exists precisely because straight lines are the flaw in every other model.

Most of them want a realreturn, after inflation, and a target in today's money. Five to seven percent is the range most people use for a globally diversified equity portfolio, based on long-run history. It is an assumption rather than a promise, and the honest way to use any of these is to run your preferred figure, then run it again two points lower and plan around the second answer.

Each tool states its own assumptions and limitations on the page, above the results rather than in a footnote. If a figure here disagrees with one you have seen elsewhere, the assumptions are almost always why, and ours are written down.