numberrule

Every formula, written out

What a return figure hides

Every projection on this site — and everywhere else — takes a single rate and applies it every year. It is the only tractable way to do it, and it quietly removes three of the things that decide how much money you end up with.

Those three are charges, the order the returns arrive in, and tax. None of them appear in a headline return figure, and all of them are larger than most people assume.

The employer match is the only guaranteed return there is

Before anything about markets, there is one return that is not a projection. An employer matching half of what you contribute up to six per cent of salary is handing you an immediate fifty per cent on the matched portion, on the day you contribute it, regardless of what anything does afterwards.

On a $75,000 salary contributing six per cent, that is $187.50 a month you would not otherwise have. Over thirty years the employer's share alone comes to $91,278.18 of contributions, and with growth the whole pot reaches $1,043,454.75 from a $25,000 starting balance.

Nothing else in personal finance pays fifty per cent guaranteed. Not contributing enough to take the full match is the single most expensive common mistake in the category, and it is entirely avoidable.

The one catch worth knowing is vesting: matched money often has to be earned over a few years of service, so leaving early can mean leaving some behind. Your own contributions are always yours.

$75,000 salary, 6% contributed, 50% match capped at 6%

You pay in $375.00 a month

Employer adds $187.50 a month

After 30 years $1,043,454.75

Of which growth $744,620.22

Work it out: 401(k) Calculator →

Charges come off the return, not the balance

A fund charging 1% a year does not cost you one per cent. It costs you one per cent of the balance every year, compounded, which over decades is a much larger share of the final total than the number suggests.

The reason is that the charge is levied on the growing balance while the growth it removes would itself have compounded. Take the projection here — $500 a month at 10% for twenty years reaching $379,684.42 — and the same plan at 9% instead finishes at $333,943.43, some $45,700 lower. That single point of difference is what an expensive fund costs against a cheap one, on $120,000 of contributions.

This is why charges are worth more attention than they usually get, and why they are the one input in an investment projection you can actually control. You cannot choose the return. You can choose what is deducted from it.

Work it out: SIP Calculator →

Regular investing removes a decision, not a risk

Paying in the same amount every month buys more units when prices are low and fewer when they are high, which takes the timing decision out of your hands. That is genuinely valuable, mostly because timing decisions made under stress are usually bad ones.

It is often oversold as risk reduction, and it is not that. It does nothing about a market that falls and stays down, and it does not make a bad investment good. What it does is stop you having to be right about when.

Over twenty years at 10%, $500 a month becomes $379,684.42, of which $259,684.42 — over two thirds — is growth. That figure assumes a steady 10% every year, before tax and before charges, which is three assumptions doing a lot of work.

The withdrawal rate is where the confidence goes

Planning to live off a portfolio inverts everything. Instead of a rate of return you need a rate of withdrawal, and the famous four per cent rule is a much weaker foundation than its ubiquity suggests.

It comes from a study of thirty-year retirements in one country over one historical period. A retirement that has to last fifty years is a different question, and the honest range of defensible rates is wider than a single figure.

The other thing that appears here and nowhere else is the order of returns. Two portfolios with identical average returns can end very differently if one has its bad years at the start, because early losses come out of a pot that is also being drawn down. While you are still accumulating, the order barely matters. Once you are withdrawing, it is one of the largest factors there is.

What does move the date reliably is the saving rate. Someone saving forty per cent of their income is both building faster and needing less to live on, so it works from both ends at once — which is why it dominates the arithmetic of independence far more than the assumed return does.

Work it out: FIRE Calculator →

Questions

What is an employer match worth?

A 50% match is an immediate 50% return on the matched contributions, guaranteed, before any market growth. On a $75,000 salary at six per cent it is $187.50 a month. Nothing else in personal finance pays that.

How much do fund charges actually cost?

Far more than the percentage suggests, because the charge is taken every year from a compounding balance. Over twenty years a single percentage point can cost tens of thousands on a modest monthly contribution.

Does investing monthly reduce risk?

It removes the timing decision, which is valuable. It does not protect against a market that falls and stays down, and it does not make a poor investment a good one.

Is the 4% rule safe?

It comes from thirty-year retirements in one country over one historical period. For a longer retirement it is optimistic, and the defensible range is wider than a single number implies.

Why does the order of returns matter?

While you are contributing, it barely does. Once you are drawing money out, early losses come from a pot that is also shrinking through withdrawals, so bad years at the start do lasting damage that good years later cannot undo.

What matters more than the return I assume?

How much you save, and what you are charged. The return is the input you have least control over and the one most projections spend all their time on.

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