Read a model that turns a savings rate and an assumed return into years to independence.
Search "FIRE calculator" and open any of the dozens of results. You type in a few numbers and a date appears, which feels like an answer. Before you trust it, look at what you had to enter and what the calculator filled in for you. The date comes from four or five assumptions, and most of them are hidden. Changing any one of them can move the date by years. The model below is the simplest useful version. It is the same model behind the figures in lesson 4.1, Savings rate works twice.
The simple model has four inputs. The first is income, which here means your yearly take-home pay. The second is your savings rate, the share of take-home pay you save and invest. Whatever you don't save, you spend, so income and savings rate together also give your yearly spending. Yearly savings are income times the rate, and yearly spending is income minus savings.
The third input is an assumed real return. This is the return after inflation, roughly the nominal return minus inflation (How money works, lesson 4.2, Real return is roughly the nominal return minus inflation). Using a real return keeps every figure at today's prices, which matches the spending base you built in lesson 1.4.
The fourth input is the target, written as a multiple of yearly spending. Lesson 2.1 showed that a 4% withdrawal rate means a target of 25 times spending. At a 3.5% withdrawal rate the multiple is about 28.6, which is 1 divided by 0.035.
Once the inputs are set, the model works through one year at a time. Each year it takes last year's balance, adds one year's return on that balance, then adds this year's savings. If the balance has reached the target, it stops and counts the years. If it hasn't, it repeats.
Take someone who takes home S$60,000 a year (an example figure) and saves 20%. That is S$12,000 saved and S$48,000 spent each year. Their target is 25 x S$48,000 = S$1,200,000. They start from zero and assume a 4% real return.
At the end of year 1 their balance is S$12,000. In year 2 the return is 4% x S$12,000 = S$480, and adding S$12,000 of savings brings the balance to S$24,480. In year 3 the return is about S$979 on S$24,480, and with another S$12,000 the balance is about S$37,459.
In the early years the yearly savings are much larger than the return, so nearly all progress comes from saving. For this person the yearly return first exceeds the S$12,000 yearly saving in year 19. The balance first passes S$1,200,000 in year 42.
Suppose the same person doubled their income and kept saving 20%. Their savings would double, but so would their spending and their target, so the number of years stays the same. For a given savings rate and return, the date does not depend on how much you earn. This is a surprising result the first time you see it, and it is the reason savings rate is the figure to watch.
You can see how much each input matters by changing one at a time. The figures below all hold the target at 25 times spending, start from zero, and use illustrative assumptions. At a 4% real return, saving 20% takes about 42 years and saving 50% takes about 18 years. The savings rate alone accounts for a gap of twenty-four years. At a 20% savings rate, a 2% real return takes about 56 years and a 6% real return takes about 34 years.
Moving the savings rate across a realistic range changes the date more than moving the return across its plausible range, which is the same pattern as in lesson 4.1. The two ranges also differ in kind. Savings rates in that range are ones people actually reach. Returns in that range are what markets may or may not deliver, and you cannot choose which you get. Every figure in the model is an output of assumptions, and none of them is a forecast.
Real returns never arrive smoothly at 4% a year. Lesson 2.3, Sequence risk: why the first years matter most, showed that the order of returns matters once you start withdrawing. While you are still saving, a bad decade can also push the date back.
The model starts from zero, and almost nobody does. Money you have already invested is a head start and can take years off the result. The model also ignores CPF, which does real work in your plan through the two-part number from lesson 3.4. It assumes your income and savings rate never change, but in real life both usually rise early in a career and may fall later.
Use the simple model to understand which lever matters, and leave the actual planning to a more detailed model. Lesson 4.4, Build your FI model, replaces it with a year-by-year sheet that uses your own balance, your own contributions and your two-part number as the target.
Before lesson 4.4, collect these figures:
Your take-home income, which you found in the lesson 4.1 exercise. Your savings rate, from the same exercise. Your current invested balance: everything you could draw on for the bridge, such as investments in your own name and money set aside for the long term. Leave out CPF and your emergency fund. A real (after-inflation) return assumption you could defend to a cautious friend, plus a lower and a higher figure to test.
The activity asks you to write them all down in one place.
Write down your income, savings rate, current invested balance and an assumed return. You will put these into the model.
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