Retirement Projection: What the Arithmetic Needs From You

A retirement projection prices a goal and tests whether the money lasts. The calculator below is given what the household would spend once the earning stops, how long until that happens, what it has put by and adds each month, how long the money must last, and rates chosen by the household itself. Over decades the rates chosen move the answer further than any amount entered, so the calculator hands back a range rather than one figure.

Almost everybody who runs this arithmetic honestly for the first time gets back a gap that looks impossible. An impossible-looking gap is the ordinary result, and the gap is a fact about a calculation stretched over twenty four years rather than a verdict on the person who ran it: a reader who is fifty with nothing set aside is reading the same arithmetic as a reader who is twenty five. Nobody can forecast what any arrangement will deliver across such a stretch, so every figure the panel below returns rests on assumptions the reader supplied.

What does this working tool compute?

The tool takes one figure and grows it, then spends the result down. The household supplies what it would spend in a month once nobody is earning, priced in today's moneyPriced at what things cost now, before any allowance is made for prices rising between now and the date under consideration., and the tool works out what that same month costs at the point the earning stops, at each rate supplied. Then it takes what has already been put by, adds what goes in each month, grows that at a rate supplied as well, and draws the spending back out year by year until either the years run out or the money does.

The tool never returns one number. Three results come back side by side with the distance between the outer two named, and that distance, rather than any of the three results, is the thing this tool exists to produce.

Ask a mason what it will cost to add a room nine years from now. The plot can be measured to the centimetre and the bricks counted exactly, and nobody can say what a brick will cost in nine years, so an honest quotation comes back as a spread. A spread is not evasion. A spread is the mason declining to invent the one input nobody has, and this calculator is that mason.

What goes in, and where does each figure come from?

Six kinds of figure go in. The retirement spendingA month of outgoings priced as though the household had already stopped earning, with the lines that end taken out and the lines that grow put in. estimate, in today's money. The years to retirementThe gap between the age on a document and the age a household is planning towards, which is a subtraction rather than a judgement.. The balance already put by, and the amount going in each month. The rates, three for prices and two for what the money earns. And the duration in retirementThe number of years a pot is asked to cover, counted from the day the earning stops to a date the household picks for itself..

Each input carries a field noteThe small line printed under an input saying where that figure is found, naming a document or saying plainly that no document carries it. underneath it. Three notes name a real document: an annual statement, a payslip, and the date of birth printed at the head of the statement. The rest say the figure is found nowhere at all. The field notes are not decoration around the inputs; they say how much weight each input can carry.

Run against the invented Bhosale household, the notes that point at paper point at ordinary paper: 36 at 31 March of year two against a household planning towards 60, Rs 4,12,000/- on a statement, Rs 6,240/- a month on a payslip. The Rs 30,000/- spending figure sits between the two kinds, built from what the household actually spends but still a judgement nobody can check.

Where does the spending estimate come from, and who is allowed to set it?

The household sets it, and nobody else can. The spending estimate is the input people expect a calculator to produce for them, and it is precisely the one no calculator can reach: a tool cannot see what a household eats, who it supports, what it pays in rent, or whether somebody's knees will need attention in fifteen years. The tool does the growing next, so the estimate has to arrive priced at today's costs. Pricing it forward first would do the growing twice.

The Bhosale household arrived at Rs 30,000/- a month by starting from the Rs 42,770/- that leaves in an ordinary month and working through it line by line. Some things fall away: the school terms end, the two-wheeler loan is long gone, and one person is no longer supported out of the same money. Some go the other way, and health spending is the honest example. The fall from Rs 42,770/- to Rs 30,000/- is not a saving the household has found; it is a different shape of month, with some lines removed and others enlarged. That is Rs 3,60,000/- a year, the version a household can check against its own experience.

The years are a subtraction and the rates are guesses, so this is the one input where an hour with the bank statements genuinely improves the answer.

How many years until the income stops, and why is that the one certainty here?

Because it is a subtraction between two dates, and both dates are things a household decides or already knows. Meghna Bhosale is 36 at 31 March of year two and the household is planning towards 60. Sixty minus thirty six is twenty four, and no assumption, opinion or market movement changes that arithmetic.

Everything else here arrives with a caveat attached and this input does not. The years to retirement is the only input that is simply true, and also the input with the most violent effect on the answer. The years are the exponent: an extra year does not add to the requirement, it multiplies it again. Changing the date a household plans towards therefore changes the arithmetic far more than revising the spending estimate by a couple of thousand rupees, and the slider on the panel above moves exactly this input.

The date is a plan, though, not a promise. Work can stop earlier than intended, through health or a business closing, and it can continue later. Ashok Bhosale runs a tailoring counter, and a counter has no retirement date printed anywhere: he can work at 62 if the work is there, and he could be unable to work at 55. The tool does not pretend the date is safe.

How long must the money last, and can anybody know that?

Nobody can know it. The duration is the input where honesty costs the most: a household has to write down a figure for something it genuinely cannot find out. Leaving the field out would only move the guess somewhere less visible, so the tool asks for it anyway. The tool refuses to fill the field in from an average. An average across a population is a statement about the population, not about the household at the screen. A figure that is unknowable is entered as a judgement and marked as a judgement, and the tool's job is to keep it marked rather than to quietly resolve it.

The duration multiplies. Across 240 months, a retirement of 20 years, Rs 76,899/- and Rs 1,90,235/- a month become Rs 1,84,55,760/- and Rs 4,56,56,400/-, and the distance between them becomes Rs 2,72,00,640/-.

Two warnings sit on that. Both totals assume nothing is earned on the money during retirement and that prices stop rising the day the earning stops. Arithmetic of that kind is not a pot size. And the duration multiplies the width along with everything else. Adding a duration to the calculation does not narrow the uncertainty; it scales it up in exact proportion.

Where does the rate come from, and why will this tool not fill it in?

From the household, and from nowhere else.

An assumed rateA figure the reader chooses, and the arithmetic is then run at that figure. Nobody is claiming it will happen, and no probability is attached to it. is a number the arithmetic is run at, not a forecast, and nothing about it says the world will behave that way. Most calculators of this shape have a rate sitting in the field when the panel loads, and a figure sitting in a field reads as the tool's own view of what is normal. A default in a rate field is a suggestion wearing the costume of a setting, and suggesting a rate across twenty four years is a forecast however quietly it is done.

So the tool asks for three rates for prices rather than one and draws all three answers together. The three carried here as an illustration are 4, 6 and 8 per cent a year, chosen to sit low, middle and high so the distance between them is visible. None is described as typical, expected, historical or reasonable. The Reserve Bank of India at rbi.org.in publishes the official series on prices in this country, and a reader who wants to know what has actually happened should read it there.

Handing the field back also changes what happens afterwards. A household that typed its own rate in asks six months later whether it still believes the figure. A household that was handed a rate remembers only the answer, so the least reliable input becomes the one nobody ever revisits.

Why does the screen keep the facts and the guesses apart?

Because the multiplication cannot tell them apart, and a reader must. Inside the calculation, Rs 30,000/- and 24 and 6 per cent are just three numbers being combined, and nothing in the arithmetic knows that one was read off a calendar and one was somebody's best attempt at the next quarter century. Nothing else carries that difference. The screen has to.

A household treats the same distinction easily enough anywhere else. The wedding hall costs Rs 40,000/-, the figure printed on the rate card. The catering will probably come to about Rs 40,000/-, a figure that felt about right last time. Nobody in the room treats those two alike. The moment they are added into one total the difference vanishes, and the total behaves in everybody's mind like the rate card rather than like the guess.

A retirement calculation does the same thing if it is allowed to, and the tool therefore splits the screen and names the document beside every figure that has one.

What does the computation actually do, step by step?

The computation multiplies one figure by one plus the rate, once for every year, and then stops. A household that can follow the arithmetic by hand has a reason to trust the output that no amount of design polish can give it.

Take the Bhosale household's Rs 30,000/- a month at 4 per cent assumed. After one year the same month costs Rs 31,200/-, after two Rs 32,448/-, after three Rs 33,746/-. Each step multiplies the previous line by 1.04, and twenty four steps give Rs 76,899/-. The balance ledger in the panel above runs on the same principle, one line a year.

Rs 76,899/- is one of three figures, and one of three is never this tool's answer. Notice what the ladder does: the first year adds Rs 1,200/-, and the year running from 23 to 24 adds close to Rs 2,958/- on a much larger base. Nothing changed about the rate. Only the base it was applied to grew, and that is the entire reason a long goal behaves differently from a short one.

Why is the output a range and never a single figure?

Because the three results are not close to each other, and picking one would be a claim the arithmetic cannot support. At the household's own 24 years, the same Rs 30,000/- month costs Rs 76,899/- on one assumption, Rs 1,21,468/- on another and Rs 1,90,235/- on the third, the highest nearly two and a half times the lowest.

A rangeSeveral results shown next to each other. No single one of them can then be read as the answer. is what is shown when the honest content of a calculation is a set of results rather than one. The tool shows all three because showing one would mean choosing between them, and that would mean holding a view about the next twenty four years that nobody holds. The arithmetic is identical in all three cases; only the assumption differs, and the assumption came from nowhere.

Single-figure answers are common elsewhere because one figure is easier to look at, easier to put in a headline and easier to remember. None of those is a reason to believe it.

What does the width of the range say?

The width says how much of the answer was arithmetic and how much of it was a choice. The widthThe distance between the outer results in a range, measuring how much the answer depends on the input nobody can look up. is a measurement of the calculation, not a measurement of the household, and once it has been seen a single-figure projection cannot be read the same way again.

Rs 1,13,336/- a month is the width at 24 years on the three assumptions carried here. Set against the Rs 42,770/- that leaves the household in an ordinary month now, the width alone is more than two and a half times its entire monthly outgoings.

At five years out the three assumptions produce Rs 36,500/-, Rs 40,147/- and Rs 44,080/-, within Rs 7,580/- of each other and practically one line on a chart. The width opens quietly and then, in the last third of the period, enormously. No year in the twenty four ever feels like the moment to react: the year-on-year difference is small enough to be lost inside ordinary price movements a household already absorbs without comment. The damage lives in the compounding and is invisible the whole time it happens.

What does the arithmetic look like on one household's numbers?

With every figure marked for what it is, the household's run looks like the table below. Read down the last column. The reliability lives there.

Beside that sit the things the household can look up: a provident fund balance of Rs 4,12,000/- at 31 March of year two, and Rs 6,240/- a month going in, being Rs 3,120/- from the employee side of Meghna Bhosale's payslip and Rs 3,120/- shown separately as the employer side, or Rs 74,880/- across a year. The balance and the contribution are the only rupee figures in the entire exercise that a household can prove, and they come off two documents it already receives.

Feed those two documents into the panel above, at 8 per cent assumed on the way up and the middle price assumption of 6 per cent, and the ledger runs 24 lines to a balance of Rs 80,11,856/- on the day the earning stops. Five of those lines are below, each carrying its own check: opening, plus added, plus growth, less drawn, equals closing, to the rupee.

At that assumption the Rs 30,000/- month has become Rs 1,21,468/-, and twelve of those is what the first year of retirement costs, so Rs 14,57,616/- is drawn. A pot of Rs 80,11,856/- sounds like a great deal of money, and against a first year costing Rs 14,57,616/- it lasts into the year that starts at 65. That is the ordinary result named at the outset.

Ashok Bhosale's version is the more important one. The tailoring counter carries no scheme of any kind: no employer side, no statement arriving once a year, no balance to enter. Having no scheme at all is the ordinary position for most self-employed people in this country, and it is not a failing or a story about somebody who did not plan. His left column has one entry in it, the years, and the rest runs exactly the same way. The arithmetic here does not require a payslip, and a household without one is running the same calculation rather than a lesser version of it.

What happens to the same plan when the price rise is left out?

The money stops running out. Leave every other figure where it is, take the price rise out of what the money has to buy, and the Rs 80,11,856/- pot never falls: a flat Rs 3,60,000/- a year comes out, more than that is credited back at the assumed 6 per cent, and the balance climbs to Rs 1,34,49,547/- by the end of the twenty fifth year. The same plan, the same pot and the same assumed return give a household that runs out of money at 65 and a household that ends richer than it retired, and the only thing that changed was an assumption the reader chose.

The button on the panel does that and nothing else, so the two answers sit side by side. The failure reads as good news: a projection which ignores the price rise returns a larger closing balance, a longer horizon and a comfortable-looking chart, and every one of those is a reason to believe it rather than to check it.

The second run really says that the money earned nothing after prices. At 6 per cent assumed on the pot and 6 per cent assumed on prices, the real returnWhat is left of a return once the rise in prices is taken out of it. A minus figure there means the money buys less each year even while the balance on the statement grows. is zero, so a balance growing by 6 per cent a year buys no more than it did. Switching the price rise off in the withdrawal while leaving it in the return quietly credits the household with a real return it never assumed.

What does the tool refuse to do?

Four things, printed on its own face rather than buried in a note at the bottom. A refusal a reader has to go looking for is not really a refusal.

The tool does not decide a rate: whatever sat in that field would be read as a view about the next quarter of a century. The tool names no scheme, fund, allocation, product or provider. The tool cannot tell a household how long it will live. And the tool will not say whether the gap it computes should be closed, or how, and the answer depends on things no arithmetic can see: what else the household is carrying, who depends on it, what work is likely to be available at 58, and what the household thinks its next twenty years are for.

The last refusal is the one people find hardest. The tool has just produced a large and uncomfortable figure and then declined to say what to do about it. Answering would require knowing what the household owes, whether somebody in it is ill, and what it has left to give up. A tool that answers anyway is guessing in the same typeface it used for the arithmetic.

Richard Thaler's work on how people treat distant outcomes describes why this goal is the last one any household costs: a cost twenty four years away feels smaller than the same cost next month. A household that has never costed this goal has not been careless, and the first honest look at the figure is where that changes.

What goes wrong when four unequal inputs come out as one number?

How does anybody actually use a width?

The width is also the reason to write the assumption down beside the answer. A sheet saying Rs 1,21,468/- has recorded the least reliable part of the calculation as though it were the most settled. A sheet saying Rs 1,21,468/- at 6 per cent assumed, with Rs 76,899/- at 4 and Rs 1,90,235/- at 8, records what actually happened, and the household can then argue with the rate rather than the amount.

What can this arithmetic not say?

The Bhosale household, Meghna Bhosale, Ashok Bhosale, Ira Bhosale and Sahyadri Freight Services Private Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.