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Wealth, Advice & Personal Finance
1Money Basics and Banking
Household Financial DocumentsHousehold ExpensesHousehold IncomeBank AccountsDigital Payments in IndiaFinancial GoalsThe Household Financial ReviewThe Household Balance SheetHow to Build a…Your Banking CredentialsOverdraftGoal HorizonGoal PlanningHousehold Cash FlowMonthly BudgetBudget vs Cash Flow
2Credit and Debt
DebtLoansLoan and EMIHow to Read a…InterestCompound InterestCredit CardsCredit Card vs Personal LoanBuy Now Pay LaterYour Credit RecordDebt ConsolidationCredit ScoreHow to Read a…The Debt TrapDebt PayoffDebt-to-Income RatioHow to Build a…
3Household Resilience
Financial ResilienceFinancial ShocksEmergency FundHousehold Net WorthHow to Prepare for…
4Insurance and Protection
Term InsuranceTerm Cover NeedInsurance Fact vs Insurance AdviceEmergency Fund vs InsuranceReading an Insurance Policy DocumentTerm Insurance vs Endowment PolicyThe Proposal FormInsurance ClaimsHealth InsuranceHow to Prepare an…Protection PlanningHow to build a…Policyholder and NomineeDeductible and Co-PaymentULIPTerm Insurance vs ULIP
5Investing Literacy
Equity for a First-Time InvestorGold in an Indian HouseholdSpeculationThe Return PromiseSIP Future ValueSavings vs InvestingRisk vs VolatilityHow Risk and Return…How Diversification Reduces Single-Exposure…
6Retirement
RetirementRetirement ProjectionHow to build a…EPFHow to Read an…PensionPension vs AnnuityGratuityInflation Risk on a Long GoalNPSHow to Read an…PPFEPF vs PPF vs NPSHow to Read a…Longevity Risk and the Withdrawal Rate
7Advice Process
Education and AdviceHow to create an…The Investor CharterFinancial AdviserFinancial IntermediariesFinancial PlanningHow to Check Whether…The Registered Investment AdviserAdviser vs Distributor vs…
8Rights and Recovery
Unfair PracticeSCORESThe OmbudsmanConsumer RedressalEscalating a Financial ComplaintHow to use SCORES…How to Escalate a…Mis-SellingMis-Selling vs Market Loss
9Fraud Awareness
Financial FraudHow to Respond to…How to Prepare a…Ponzi SchemesPonzi Scheme vs Regulated InvestmentHow to Recognise a…Financial InfluencersSocial EngineeringReturn and Performance ClaimsFinancial Red Flags

How to Read a PPF Account Statement, Line by Line

A public provident fund (PPF) statement shows an opening balance, every deposit with its date, and a credit added once at the end of the year. The credit is computed on the lowest balance held between the fifth of each month and its end, so the statement can be checked line by line, and the date beside each deposit is part of the arithmetic rather than a record of it.

Almost everything a household receives in a year arrives already decided. The electricity bill rests on a tariff the household did not set, the school fee circular on a decision taken in a meeting nobody from the household attended, the hospital estimate on a rate card nobody will show. All three can be asked about. None of them can be rebuilt at a household's own table with a pen.

A public provident fund statement can be rebuilt. The statement carries a figure the year started from, a list of what went in and when, and a figure added once at the end. No manager makes a call, no price moves overnight and no valuation has to be taken on trust. Every figure follows from the figures above it by addition and one multiplication. Addition and one multiplication make this the only document in the whole sequence a household can recomputeWorking a figure out from the document in front of the reader, rather than accepting it because it is printed. from end to end, and it is still the document most households have never sat down with.

Not sitting down with it is entirely ordinary. The statement describes money that cannot be spent this month, and nothing in a normal week depends on whether it is right. Richard Thaler and the behavioural work that followed him named the pattern: people discount a distant outcome far more steeply than a near one, and a document about a distant outcome inherits the discount. There is nothing careless in it.

Forty minutes, once, with one statement and a sheet of paper, and a balance is never again read as though the balance were the whole story. The single most useful thing to be learned from a document like this is that a balance and a result are two different quantities, and that on this particular document the difference between them is a figure the household can work out itself.

One caution about scale comes before anything else. The scale decides how the rest of the arithmetic should be read. The specific timing lesson at the centre of this statement is worth about six rupees over a whole year. Six rupees is not a mistake in the arithmetic. Six rupees is the honest size of the effect, and inflating it into a warning would be exactly the fault this sequence objects to everywhere else.

What is assumed here, and what must be confirmed at source?

Every figure of arithmetic below runs on an assumed rateA rate chosen so the arithmetic can be followed all the way through. It is a teaching device, not the figure any scheme actually uses. of 7 per cent a year, and therefore 0.5833 per cent a month. The 7 per cent is an assumption, chosen because it divides cleanly by twelve and because a reader needs some number to follow the working with. The scheme's own rate is a different figure, set by the government, and nothing about that rate should be read into the choice made here. The assumption is named again beside every amount it produces.

The scheme's actual rate is set by the government and revised from time to time. The deposit limit, the term, the lock-in period, the withdrawal conditions, the loan conditions and the tax treatment are set the same way, by rules that change. The Ministry of Finance decides the small savings arrangements and the Reserve Bank of India publishes at rbi.org.in. Each of those is worth confirming at source, at the moment it is needed.

The shape of the document is not assumed. The order of its lines, the fact that deposits carry dates, the fact that a credit lands once rather than continuously, and the fact that the whole thing reconciles are properties of this kind of statement rather than choices made here.

One more thing to say plainly at the start. Ashok Bhosale, who runs a tailoring counter, receives no statement of this kind at all, and neither does anyone else whose work carries no scheme with it. Most self-employed people in this country are in that position, and a statement of this kind sits in far fewer drawers than the arithmetic below might suggest. For a reader without any such account, the mechanism is still worth twenty minutes: a rule about which balance a calculation looks at turns up in more places than this one.

What does this statement actually show, line by line?

The whole document is worth taking in at one look before any part of it is read. There are five kinds of line on it and no more, and knowing that there are only five is most of the battle. A document whose parts cannot be named feels much longer than it is.

The first kind is identity: whose account this is and which stretch of time the paper covers. The second is the opening balanceWhat the account held at the start of the period the statement covers, carried in from everything that happened before it., one figure, at the top. The third is the deposits, one line each, every line carrying a date. The fourth is the balance those deposits and the opening figure add up to. And the fifth is the creditThe amount the scheme adds to the account, worked out from the balances held through the year and placed in the account once, at the year end.. The scheme adds the credit once, and it is the only line the household did not put there itself.

On Meghna Bhosale's statement the five come out like this. The account is hers. The financial yearThe stretch of time a statement covers. For an account of this kind it runs from the first of April to the thirty first of March following. covered runs from 1 April to 31 March. The opening balance is Rs 72,000/-. There are twelve deposits of Rs 1,000/- each. The balance on 31 March is Rs 84,000/-. And the credit, at the assumed 7 per cent a year, comes to Rs 5,489/-. Not one paisa of it appears inside that Rs 84,000/-.

Five kinds of line, and one of them is not filled in yet. AN INVENTED STATEMENT FOR AN INVENTED HOUSEHOLD. THE CREDIT SHOWN RESTS ON AN ASSUMED 7 PER CENT A YEAR AND ON NO ACTUAL RATE. PUBLIC PROVIDENT FUND, ACCOUNT STATEMENT Account holder: Meghna Bhosale Year covered: 1 April to 31 March, both dates included Opening balance, 1 April Rs 72,000/- DEPOSITS, EACH ONE CARRYING THE DATE IT WENT IN 3 April, deposit Rs 1,000/- 3 May, deposit Rs 1,000/- 3 June, and so on through October, six lines more Rs 1,000/- each 20 November, deposit Rs 1,000/- 3 December, and so on through February, two lines more Rs 1,000/- each 3 March, deposit Rs 1,000/- Twelve deposits, added up Rs 12,000/- Balance shown on 31 March Rs 84,000/- Credit for the year, placed once at the year end Rs 5,489/- Closing balance once the credit lands Rs 89,489/- 1 Whose account is this, and which year? 2 What did the year start from? 3 What went in, and on exactly which day? The red row is dated the 20th. 4 A balance. Not a result, and not the year's answer. 5 The only line the household did not put there itself. 6 The one line that has to reconcile exactly. EVERY RUPEE FIGURE HERE IS INVENTED FOR TEACHING.
Six questions sit on one sheet of paper, and only the last of them is about the number most households go straight to, which is why a reading order beats a glance.

Look at what the callouts on the right are doing. Each line is not a fact waiting to be absorbed, it is a question waiting to be asked. A household that opens this document, reads Rs 84,000/- and shuts it again has answered one question out of six, and has answered the one carrying the least information.

The most important structural fact about this document is that the credit is worked out twelve times and paid once, so the balance in the account climbs as a staircase and then takes a single large step at the year end. On every day of the year before the credit lands, the balance is nothing but the deposits. Nothing is wrong on any of those days.

Twelve calculations nobody sees. One credit, once, at the end. ALL TWELVE AMOUNTS COME FROM AN ASSUMED 7 PER CENT A YEAR AND FROM NO ACTUAL RATE. APR 425.83 MAY 431.67 JUN 437.50 JUL 443.33 AUG 449.17 SEP 455.00 OCT 460.83 NOV 460.83 DEC 472.50 JAN 478.33 FEB 484.17 MAR 490.00 ONE CREDIT: Rs 5,489/-, ADDED ONCE WHAT THE BALANCE DOES ACROSS THE YEAR 72,000 84,000 89,489 1 April 31 March THE DASHED LINE IS WHAT A GRADUAL BUILD WOULD LOOK LIKE. IT IS NOT WHAT HAPPENS HERE. ONE STEP OF Rs 5,489/-, RIGHT HERE, AND NOT A RUPEE OF IT BEFORE. Rupee amounts on both panels are invented for teaching and rest on the assumed rate.
Twelve monthly amounts are worked out through the year and none of them is paid until the last day, so the balance climbs in small equal steps and then jumps once.

The dashed line on the lower panel matters more than it looks. The gentle slope is what most people picture when they think of an account earning something, and it is a fair picture of a great many arrangements. A public provident fund account is not one of them. Here the amount is being worked out continuously and handed over discontinuously, and the distance between those two facts is the source of nearly every misreading of this document.

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Where does the Rs 72,000/- opening balance come from?

The opening balance comes from before. Three words are the entire answer. The opening balance is the one line on this document that has nothing to do with the year being reported, and the account is handing itself forward.

A statement covers a period, and a period has a beginning. Everything that happened in the account before 1 April, however many years of it there were, arrives on the statement compressed into one figure and is never itemised again. Meghna Bhosale opened this account some years ago, deposited into it in a way that was probably less tidy than the twelve neat lines below, and received a credit at the end of each of those years too. All of it is now Rs 72,000/-.

The khata book at a shop where a household runs a monthly account works the same way. Every new sheet starts with the words previous balance and one figure, and nobody expects the shopkeeper to copy out last month's items. The new sheet is about this month. The figure at the top is the handshake between the two.

The opening balance does two jobs at once. Everything printed below it is an addition to it, so it anchors the reading, and it is the one figure on the whole statement that can be checked against a document produced at a different time. Last year's statement, if the household kept it, ends at a closing balance. The new statement begins at an opening balance. The two must be the same figure, and if they are not, something specific, dated and findable has been found.

If the household did not keep last year's statement, that is completely ordinary and nothing is lost. The check simply waits a year. The closing figure of this year becomes next year's opening one, and from that point onward the household has a chain rather than a stack. A folder with a decade of these in it is a full history of an account and costs nothing but the folder.

One piece of continuity worth pausing on. The sheet the Bhosale household drew up for itself carries a public provident fund holding of Rs 84,000/-. The sheet's figure is this statement's 31 March balance, entered honestly, and it is also Rs 5,489/- short of the amount the account is about to hold. Nobody made an error. The sheet recorded a balance, and a balance was all there was to record on that date.

Try it out

The opening balance on this statement is Rs 72,000/-. Where did that figure come from?

What do the twelve deposit lines record, and why does each carry a date?

Below the opening balance sit twelve lines, one for each deposit. Each line carries two things: an amount and a date. Most people read the amount and skip past the date, on the reasonable assumption that a date on a document is filing information. On this document it is not. The date is an input to the arithmetic, in the same way the amount is.

The amounts come first, being the easy half. Twelve deposits of Rs 1,000/-. The deposits come to Rs 12,000/- across the year, and the first check on this block of the statement is simply to count the lines. Twelve lines, twelve months, no month missing and no month appearing twice. A missing line is a much larger question than a mis-stated one. If a household deposits monthly and finds eleven lines, that is worth a look before anything else on the statement is read.

Now the dates. Eleven of Meghna Bhosale's deposits are dated the third of the month. One, in November, is dated the twentieth. The statement never says why, and no statement of this kind ever does. Somewhere in that November there was a wedding to contribute to, or a repair, or a fortnight where the deposit was not the first thing on anybody's mind. The reason is not knowable from the document, and it is not a matter for disapproval. The late deposit happened in a household depositing every single month of the year. Twelve deposits is more than most households manage, and the late date turns out to have cost about the price of a bus ride.

The date beside a deposit is a working input rather than a record of when the paperwork happened, and that single fact separates people who can rebuild this statement from people who can only read it. The word used for it, where a document bothers to use one, is the value dateThe date from which a deposit is treated as being in the account for the purpose of a calculation. It need not be the day the money physically moved.: the date a deposit counts from, and not always the day it left the household's hands.

Ashok Bhosale keeps a version of this at the tailoring counter without ever calling it anything. Every garment taken in gets a date written beside it in the register, and the date decides the delivery, not the garment. Two identical shirts brought in nine days apart are the same work and two different promises. The register is not recording history there; it is recording an input. A deposit line on this statement is doing the same job.

Two things are worth checking on the deposit block, and both are quick. First, that each amount matches what actually left the household's bank account. The bank's own record already shows it. Second, that each date is the date the money left, or close to it. A gap of a few days usually has an ordinary explanation, but it is worth noticing once. A household then knows how its own money travels.

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Why does the balance on 31 March have no credit in it?

More households leave this document disappointed over one question than over any other. The account started the year at Rs 72,000/-. Twelve thousand rupees went in. On 31 March the statement reads Rs 84,000/-. Where is the growth?

The growth has not happened yet, in the only sense the statement cares about. The credit is worked out from the balances the account held month by month, and it is placed in the account once, at the end of the year. On 31 March, before that placement, the balance is exactly what it looks like: the opening figure plus the deposits. Rs 72,000/- plus Rs 12,000/-. There is no third component in it and there is not supposed to be.

The arithmetic that goes wrong takes four seconds and is completely rational, and being rational is exactly why it is so common. Subtracting the opening figure from the closing figure gives Rs 12,000/-, exactly what the household deposited. The obvious conclusion is that the account earned nothing at all in twelve months, and a household reaching it has every reason to wonder why it bothered.

Nothing in that reasoning is careless; it is simply a subtraction performed on a date when one of the two components had not been added yet. The same subtraction done a day or two later, once the credit has landed, gives Rs 17,489/- and tells a completely different story with the same account and the same deposits.

The balance on 31 March holds no credit at all, and it is not meant to. INVENTED FIGURES. THE CREDIT SHOWN RESTS ON AN ASSUMED 7 PER CENT A YEAR AND ON NO ACTUAL RATE. WHAT THE STATEMENT PRINTS ON 31 MARCH: Rs 84,000/- Rs 72,000/- Rs 12,000/- put in this year Rs 5,489/- still to be added, not in the balance CARRIED IN FROM EARLIER YEARS THE READING THAT GOES WRONG Rs 84,000/- minus Rs 72,000/- is Rs 12,000/-, which is exactly what was deposited. So the account did nothing at all for twelve months. CORRECT SUBTRACTION. WRONG DAY. WHAT IS ACTUALLY THE CASE A balance is a balance. The credit is placed once, at the year end, and comes to Rs 5,489/- here on the rate assumed here. SAME ACCOUNT. SAME DEPOSITS. A BALANCE AND A RESULT ARE TWO DIFFERENT QUANTITIES ON THIS DOCUMENT. Every rupee figure on this drawing is invented for teaching and no actual rate is stated anywhere.
The printed balance stops where the deposits stop, so a household subtracting one figure from the other measures its own deposits and calls the answer a return.

The misreading this document invites, and what it costs

A household opens the statement in April, sees Rs 84,000/-, subtracts the Rs 72,000/- it remembers from last year, gets Rs 12,000/-, and concludes that a year of monthly discipline produced nothing whatever. The conclusion is arithmetically clean and completely wrong, and it does real damage. The household that reaches it is the household that quietly stops depositing. The mistake is not in the subtraction; it is in reading a balance as though a balance were a result, on a document where the two are kept separate.

The closing balanceThe opening balance plus every deposit plus the credit, being the figure the account actually holds once the year end has passed. is the figure to compare against, and it is Rs 89,489/-. The closing balance is Rs 17,489/- more than the year started with, against Rs 12,000/- put in. The gap between those two ways of reading the same twelve months is Rs 5,489/-, and it is entirely a question of which day the subtraction was performed on.

Try it out

The balance printed on 31 March is Rs 84,000/-. How much of the year's credit is sitting inside that figure?

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Which balance does each month's calculation actually use?

Every month, one figure is picked out of that month and used. Not the balance at the start of the month, not the balance at the end, and not the average across it. The figure used is the lowest balance the account held across a particular stretch of the month, and in this guide that stretch runs from the fifth to the last day.

Two separate ideas are hiding in that sentence, so say it slowly. The first is that the rule looks at a lowest point rather than a level. The rule is watching for the worst moment inside a window. The second is that the window does not start at the beginning of the month. The window starts partway in, and anything that arrives after it has begun is simply not part of that month's answer, however much of the month is left to run.

The lowest point idea turns up in ordinary life more often than people notice. A water tank serving a building overnight is judged by the level it falls to at four in the morning, not by how full it was at eight in the evening. Filling it again at six does not help the four o clock problem. A rule watching for a low point is asking what the account could be relied on to hold right through.

April is the simplest month on the statement and is worth working through. The account starts April at Rs 72,000/-. On the third, Rs 1,000/- goes in, taking it to Rs 73,000/-. From the third onward, nothing moves. So the lowest balance held anywhere between the fifth and the thirtieth is Rs 73,000/-, and that is the figure April's calculation uses. Multiplied by 0.5833 per cent, the monthly equivalent of the assumed 7 per cent a year, April contributes Rs 425.83.

One month, one figure: the lowest point inside the stretch that counts. THE 0.5833 PER CENT A MONTH IS AN ASSUMPTION MADE HERE AND IS NOT ANY SCHEME RATE. THE BALANCE AXIS IS NOT DRAWN TO SCALE. APRIL, DAY BY DAY THE 5th, WHERE THE STRETCH THAT COUNTS BEGINS THE LOWEST BALANCE HELD ANYWHERE IN THIS STRETCH IS Rs 73,000/- Rs 73,000/- Rs 72,000/- 1 5 10 15 20 25 30 3 APRIL, Rs 1,000/- GOES IN Rs 73,000/- multiplied by 0.5833 per cent, which is what an assumed 7 per cent a year comes to in one month gives Rs 425.83, and that is the whole of April's contribution to the year's credit.
The rule watches for the lowest point inside a window rather than the level at either end, so a deposit that lands before the window opens counts for the whole month.

Now hold the shape of that picture in mind. April's shape is the shape of all twelve months. The balance walks along at whatever it walked in with. If a deposit lands before the window opens, the whole month is calculated on the higher figure. If it lands after the window opens, the month is calculated on the lower figure and the deposit waits for next month to be noticed, even though the money is unquestionably sitting in the account the whole time.

The rule is not asking what the account held at any particular moment; it is asking what the account could be counted on to hold right through the stretch it looks at. A late deposit is therefore present in the account and absent from the arithmetic at the same time. That is not a trick and nothing is being withheld. The rule is one specific, published, checkable definition of which figure gets multiplied.

The minimum balanceThe lowest amount an account holds across the stretch of time a rule looks at, rather than at the start or the end of it. idea is worth carrying away even by a reader who never sees a statement like this one. Any arrangement paying on a minimum rather than an average is saying in advance that the timing of movements into and out of it matters. Once the habit of asking which balance a calculation uses is formed, it gets asked of everything, and about half the time the answer surprises.

India

Where the rules behind this document actually sit

In India the public provident fund is a small savings arrangement of the central government. The Ministry of Finance decides its terms. The Reserve Bank of India publishes at rbi.org.in the material a household would look at for the current position. Everything that could be described as a number in the scheme is set there and every one of those numbers can change.

All of them are the scheme's to set and to change: the rate, the deposit limit for a year, the term, the lock-in period, the withdrawal conditions, the loan conditions and the tax treatment. The 7 per cent a year used throughout is an assumption, adopted purely so a reader can follow arithmetic from one end to the other. The stretch the rule looks at runs here from the fifth of the month to its end, a choice that makes the worked example legible; the exact stretch is likewise set by the scheme. All of it can be confirmed at the Ministry of Finance and at the Reserve Bank of India at rbi.org.in.

Where a scheme of this kind touches tax, the Central Board of Direct Taxes publishes at incometaxindia.gov.in. Where an employer scheme is concerned, the Employees' Provident Fund Organisation publishes at epfindia.gov.in, and where the National Pension System is concerned, the Pension Fund Regulatory and Development Authority publishes at pfrda.org.in. Both are different arrangements with different documents, and both are covered separately.

Try it out

October and November both work out on a figure of Rs 79,000/-, even though a deposit went into the account in November. Why?

How is the credit worked out, month by month?

Twelve times over, the same three steps. The balance the month was carried into is the starting figure. The deposit is added if it landed before the stretch that counts had begun, and left out if it landed after. Whatever that leaves is multiplied by the monthly figure, here 0.5833 per cent, taken from the assumed 7 per cent a year. The answer is written down, and the next month follows.

There is no fourth step and there is nothing hidden inside any of the three. Three plain steps are the whole reason this document is worth a household's evening: the credit at the bottom is not a figure somebody else worked out and expects to be believed, it is a figure a household can arrive at with a pen, and arriving somewhere else means something worth asking about has been found.

Three steps, twelve times, and every input is printed on the statement. THE 0.5833 PER CENT A MONTH IS AN ASSUMPTION MADE HERE AND IS NOT ANY SCHEME RATE. BALANCE CARRIED INTO AUGUST Rs 76,000/- DEPOSIT ON 3 AUGUST, BEFORE THE 5th, SO IT COUNTS Rs 1,000/- LOWEST BALANCE IN THE STRETCH THAT COUNTS Rs 77,000/- TIMES 0.5833 PER CENT, THE ASSUMED FIGURE Rs 449.17 AND THEN THE SAME THREE STEPS, ELEVEN TIMES MORE, LAID END TO END Each segment below is one month, drawn as wide as that month's own amount. The twelve laid end to end are the year's credit. THE PALE SEGMENT IS NOVEMBER, WHICH IS THE ONLY MONTH NO WIDER THAN THE ONE BEFORE IT. APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR TWELVE SEGMENTS, ONE SUM: Rs 5,489/- NOT ONE INPUT IN THIS WHOLE CALCULATION COMES FROM OUTSIDE THE DOCUMENT. Opening balance, twelve dated deposits, one assumed rate the reader supplies. That is the complete list of ingredients. Every rupee figure on this drawing is invented for teaching.
Each month contributes a slightly wider slice than the one before it, except November, which repeats October exactly and is the only flat spot in the year.

Here is the whole thing as a ledger. Every column is either printed on the statement or worked out from the column beside it, and the last column is the one that matters. Covered with a hand, it can be produced again from the columns to its left.

MonthDeposit dateBalance carried inLowest balance in the stretch that countsAmount at the assumed rate
April3rdRs 72,000/-Rs 73,000/-Rs 425.83
May3rdRs 73,000/-Rs 74,000/-Rs 431.67
June3rdRs 74,000/-Rs 75,000/-Rs 437.50
July3rdRs 75,000/-Rs 76,000/-Rs 443.33
August3rdRs 76,000/-Rs 77,000/-Rs 449.17
September3rdRs 77,000/-Rs 78,000/-Rs 455.00
October3rdRs 78,000/-Rs 79,000/-Rs 460.83
November20thRs 79,000/-Rs 79,000/-Rs 460.83
December3rdRs 80,000/-Rs 81,000/-Rs 472.50
January3rdRs 81,000/-Rs 82,000/-Rs 478.33
February3rdRs 82,000/-Rs 83,000/-Rs 484.17
March3rdRs 83,000/-Rs 84,000/-Rs 490.00
Twelve monthseleven on the 3rd, one on the 20thRs 12,000/- depositedrounded to the nearest rupeeRs 5,489/-

Read the fourth column downward and the story of the year is there. A thousand rupees keeps arriving before the stretch that counts opens, so every figure rises by Rs 1,000/- on the one before it. Except once: between October and November the column does not move, and that is the only place in twelve months where it does not.

Twelve amounts, computed one at a time and added once, come to Rs 5,489/-, so the closing balance is Rs 84,000/- plus Rs 5,489/-, or Rs 89,489/-. Rs 89,489/- is the account's actual position at the moment the year turns, and it is Rs 17,489/- above where the year started against Rs 12,000/- deposited.

A careful reader will notice the rounding. The twelve amounts, kept to the paise, add to Rs 5,489.17, or Rs 5,489/- to the nearest rupee. Whether a scheme rounds each month or only at the end is the scheme's own rule. The size of anything hanging on it is a few paise, and knowing that saves an evening spent hunting for it.

Try it out

The twelve monthly amounts in the last column are added together once. What do they come to?

Which single deposit changed the answer, and by how much?

November. And only November, the part most worth noticing.

Look again at what happened. The seven deposits before it had landed on the third of their month and each was counted in the month it arrived in. The November deposit landed on the twentieth. By then the stretch that counts had been open for a fortnight, and the lowest balance the account had held inside it was Rs 79,000/-, reached on the fifth and held until the money arrived. Arriving late does not undo a low point that has already happened.

So November was worked out on Rs 79,000/-, exactly as October had been, and the two months produced exactly the same amount: Rs 460.83 each. The Rs 1,000/- was in the account from the twentieth of November onward. The thousand rupees was simply not part of November's answer. The deposit joined the calculation in December, where the balance carried in was Rs 80,000/- and the December deposit took the counting figure to Rs 81,000/-.

One deposit's date changed one month's figure and left every other month exactly where it was. The whole effect is a single flat spot in a column that otherwise climbs by Rs 1,000/- a step. The account did not lose the money, the deposit was not rejected, and nothing needs to be corrected. One month was calculated on a figure a thousand rupees lower than it would otherwise have been.

Two months, the same figure, and only one of them had a reason. ALL AMOUNTS REST ON AN ASSUMED 7 PER CENT A YEAR. THE BALANCE AXIS IS NOT DRAWN TO SCALE. OCTOBER deposit on the 3rd Rs 460.83 LOWEST INSIDE THE STRETCH THAT COUNTS: Rs 79,000/- 1 5 10 15 20 25 30 NOVEMBER deposit on the 20th Rs 460.83 LOWEST INSIDE THE STRETCH THAT COUNTS: Rs 79,000/- AGAIN IN THE ACCOUNT FROM THE 20th, OUTSIDE THIS MONTH'S ANSWER 1 5 10 15 20 25 30 WHAT THE DATE MOVED, AND NOTHING ELSE IT MOVED Rs 466.67 if the deposit had been on the 3rd Rs 460.83 as it actually was, on the 20th Rs 5.83 the entire difference, which rounds to Rs 6/- AND ELEVEN OTHER MONTHS COMPLETELY UNCHANGED. Every rupee figure on this drawing is invented for teaching and rests on the assumed rate.
October and November work out to the same figure because the November deposit arrived after the month's low point had already been set, and no other month is touched.

Notice how contained it is. There is a version of this rule that would compound across the year, knocking a rupee off every month after November as well. Compounding is not what happens. December carried in Rs 80,000/- either way: the money did arrive, and it arrived before December. The effect is one month wide and it closes behind itself.

Try it out

The panel below is worth an answer committed to before it is touched. The November deposit went in on the twentieth instead of the third. Across the whole year, what did that date cost?

Play with it

Slide the deposit day across the month and watch eleven markers cross the line at once.

One thing moves: the day of the month the deposits are made, from the 1st to the 28th. One thing never moves: the Rs 1,000/- going in twelve times, whatever day it is. Each strip below is one month drawn from the 1st to the 28th, with the days up to the fifth in pale green. Watch the markers change colour as they cross. November has its own control, dated the twentieth as the statement has it, and at the default setting the panel reproduces the worked example exactly.

November keeps its own date unless the setting below says otherwise.
ONE THING MOVES: THE DAY OF THE MONTH THE DEPOSITS ARE MADE. ARITHMETIC ON AN ASSUMED 7 PER CENT A YEAR, CHOSEN FOR ILLUSTRATION. IT IS NOT ANY SCHEME RATE AND NOT A FORECAST. days 1 to 5: a deposit landing here counts in this month day 6 onward: it waits for the following month APRIL TO SEPTEMBER OCTOBER TO MARCH APR Rs 425.83 MAY Rs 431.67 JUN Rs 437.50 JUL Rs 443.33 AUG Rs 449.17 SEP Rs 455.00 OCT Rs 460.83 NOV Rs 460.83 DEC Rs 472.50 JAN Rs 478.33 FEB Rs 484.17 MAR Rs 490.00 HOW FAR BELOW THE BEST THE SAME TWELVE DEPOSITS COULD DO SCALE: NIL TO Rs 70/- Rs 6/- BELOW THE BEST, WHICH IS THE COST OF NOVEMBER BEING DATED THE 20th. THE YEAR'S CREDIT: Rs 5,489/-. THE CLOSING BALANCE: Rs 89,489/-. Eleven deposits on the 3rd and November on the 20th, which is the statement exactly as it was issued.
Deposit day
the 3rd
Months counted in time
11 of 12
The year's credit
Rs 5,489/-
Below the best possible
Rs 6/-
Closing balance it gives
Rs 89,489/-
Widest the date can move it
Rs 70/-
Educational illustration. The arithmetic in the panel rests on an assumed rate rather than on any rate a scheme has declared. The 7 per cent a year, and the 0.5833 per cent a month that follows from it, are figures chosen so a relationship can be shown; neither is any scheme's rate and neither is described as typical or expected. The amount going in is Rs 1,000/- a month at every setting, so the only thing moving is the date. The differences are small and are stated in rupees rather than in shares for exactly that reason: across a whole year the widest the date can move the credit is Rs 70/-. The deposit limit, the term, the lock-in, the withdrawal conditions, the loan conditions and the tax treatment are all set by the scheme and sit outside this arithmetic.

The settings the panel passes through are worth having as plain text as well, so they survive with the panel shut. With eleven deposits on the third and November on the twentieth, the statement exactly as issued, the credit is Rs 5,489/- and the closing balance Rs 89,489/-. Move November to the third as well and the credit becomes Rs 5,495/-, or Rs 6/- more. Move every deposit to the sixth or later and it becomes Rs 5,425/-, or Rs 70/- below the best. Rs 70/- is the whole width of the effect, in a year in which Rs 12,000/- was deposited.

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What did that date actually cost, in rupees?

Rs 5.83, rounding to Rs 6/-. The six rupees is the whole of it, for the whole year.

Six rupees is a figure worth sitting with. Most explanations of this rule do not supply one at all. Such explanations say the timing matters, they say to deposit early, and they leave the size to the reader's imagination, and imagination fills it in as something much larger than six rupees. A household told that timing matters and not told by how much has been handed an anxiety instead of a fact.

Here is the arithmetic in one line, and it is the same arithmetic as everywhere else in this guide. November counted on Rs 79,000/- rather than Rs 80,000/-. The difference is Rs 1,000/- for one month at 0.5833 per cent, the assumed monthly figure, and that comes to Rs 5.83. No other month was affected, so no other month adds anything. Rs 5.83 is the complete answer and rounding it to the nearest rupee gives Rs 6/-.

The rule is worth knowing because it is free, not because it is large. BOTH FIGURES REST ON AN ASSUMED 7 PER CENT A YEAR AND ON NO ACTUAL RATE. THE TWO YEARS, DRAWN ON ONE SCALE Rs 5,495/- Rs 5,489/- every deposit on or before the 5th the statement as it actually reads, with November on the 20th THE GAP BETWEEN THOSE TWO BARS IS Rs 6/-. AT THIS SCALE IT IS THINNER THAN THE LINE DRAWN AROUND THEM. WHY THE RULE IS WORTH KNOWING The deposit was going in anyway. Making it a fortnight earlier costs the household nothing whatever. A FREE GAIN IS WORTH TAKING, WHATEVER ITS SIZE. WHY IT IS NOT WORTH REARRANGING FOR Rs 6/- across a whole year is about one bus fare across town. Nothing in a month should be moved for it. AND NO REARRANGEMENT IS CALLED FOR. SCALE IS PART OF ACCURACY. Overstating a small figure to make a rule sound important is the thing this sequence objects to throughout. Every rupee figure on this drawing is invented for teaching.
Drawn honestly on one scale the two years are indistinguishable, which is the finding rather than a failure of the drawing.

So why teach the rule at all, if the whole of it is six rupees? Because of what it costs to act on, not because of what it pays. The deposit was going in. Nobody was choosing between the twentieth and not depositing at all. If the household happens to be at the counter on the second, or sets a standing instruction for the first rather than the fifteenth, the gain arrives without anybody paying anything for it. A gain that costs nothing to take is worth taking whatever its size, and that is a completely different claim from saying the gain is large.

And now the part to state as flatly as it can be stated. No household needs to reorganise a month around the fifth. Moving a deposit earlier is not worth it if that leaves the money short somewhere else in the first week, or if the deposit only becomes possible once a payment arrives, or if the fifteenth is simply the day the household has always used. All those circumstances are worth more than six rupees. The fact and the size of the fact are what stand here, and what is done with them is nobody's decision but the household's.

The Bhosale household's November is a good example of exactly that. Something in that November made the deposit a fortnight late, and whatever it was, it was almost certainly worth more than Rs 5.83 to attend to. The household deposited in all twelve months of the year. Twelve is more than most households manage, and the arithmetic here finds nothing to criticise in it at all.

The second misreading, which is the opposite of the first

The first misreading is a household concluding the account did nothing. The second is a household concluding that the fifth of the month is a deadline to be managed. Both come from the same place: a figure read without its size attached. An explanation that presented Rs 6/- as a serious loss would be teaching a household to run its month around an amount smaller than a bus fare, and would be misleading exactly the reader it claims to be helping.

The tell for this kind of writing is easy to spot once it is known: a rule stated with urgency and no rupee figure anywhere near it. Any source that says the timing is important and cannot say the amount at stake is asking for action on an intuition rather than a figure. The habit of asking for the amount is more valuable than the small rule it is being practised on here.

Try it out

Given all of that, should a household rearrange its month so that every deposit lands before the fifth?

Rebalancing: When, Why and What It Costs teaches you to choose a rebalancing rule and say what it buys and what it costs.

What is worth checking every time this document arrives?

Four things, and the fourth is the one that earns its place. The first three check parts of the statement. The fourth checks the whole of it at once, and it is the only line on the document that has to come out exactly.

Check one is counting. Twelve months in the year, so twelve deposit lines if the household deposits monthly. A missing line is a bigger question than a wrong figure. A wrong figure is an argument about arithmetic, and a missing line is money that may not have arrived where it was sent. A household depositing irregularly counts what it remembers doing instead, a rougher version of the same check.

Check two is comparison against a second document. Every deposit left a bank account, and that account produces its own record with its own dates. The two go side by side, once. Check two is the only one that uses a document made by somebody other than the scheme. Only check two can catch an error the statement cannot see about itself.

Check three is the join to last year. The opening balance on this statement should be identical to the closing balance on the last one. Check three takes ten seconds and joins two years into a chain.

Check four is the identity: opening balance plus deposits plus credit must equal the closing balance, exactly, with no rounding of anything except the credit itself. Rs 72,000/- plus Rs 12,000/- plus Rs 5,489/- is Rs 89,489/-. If that does not come out, something on the document is wrong and it is worth finding out what.

Three checks test parts of the paper. The fourth tests all of it at once. INVENTED FIGURES. THE CREDIT RESTS ON AN ASSUMED 7 PER CENT A YEAR AND ON NO ACTUAL RATE. THE ONE LINE ON THIS DOCUMENT THAT MUST HOLD EXACTLY OPENING BALANCE Rs 72,000/- + TWELVE DEPOSITS Rs 12,000/- + THE CREDIT Rs 5,489/- = CLOSING BALANCE Rs 89,489/- 1 Count the deposit lines. Twelve months of depositing means twelve lines, and none of them missing. 2 Compare each deposit against the bank record: same amount, same date, no surprises. 3 Match this opening balance against last year's closing balance. They must be the same figure. 4 Add the four figures above. They have to reach the closing balance exactly. CATCHES THE MOST IF IT DOES NOT COME OUT, THE SIZE OF THE GAP USUALLY NAMES THE PROBLEM. A gap of Rs 1,000/- is one whole deposit. A gap of about Rs 5.83 is one month of timing. A gap of Rs 12,000/- is the year. Every rupee figure on this drawing is invented for teaching.
Adding the four printed figures is the only check that tests the document as a whole, and the size of any gap it leaves usually names what is missing.

The identity turns a bad feeling into a specific question. Suppose the four figures do not reach the closing balance. The gap is not a mystery, it is a clue with a size. Rs 1,000/- means a deposit is unaccounted for. Something near Rs 5.83 means a month of timing was handled differently from the way it is handled here. Rs 12,000/- means the whole year of deposits is not where it was assumed to be.

None of these four checks requires anything the household does not already have, and that is the reason they are worth doing at all. A statement, last year's statement if it was kept, a bank record that arrives anyway, and a pen. Nobody has to be telephoned and nothing has to be requested.

Try it out

Which of the four checks catches the most, and why?

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What does this statement not tell the reader?

A great deal, and being precise about it matters. The confidence a reconciled document gives is easy to spend in the wrong place.

The statement does not say what next year's credit will be. It cannot. Next year's credit depends on a rate nobody has announced yet and on deposits nobody has made yet. Any calculation about next year is arithmetic on an assumption, exactly as everything in this guide has been, and it deserves the same label in a household's own notes as it has been given here.

The statement does not say whether the account is a sensible place for the money. Sensible for whom is a question about the household, about what else it needs the money for, about when it might need it back and about what it holds elsewhere. The statement is silent on all four, and correctly so. A document that records cannot decide.

The statement does not say what the balance will buy. Rs 89,489/- is a figure in today's rupees, and its usefulness in twenty four years is a question about prices, a subject with its own assumptions and no answer available from a statement of deposits.

And it does not say whether the household is doing enough. Whether the household is doing enough is the question almost everybody actually brings to a document like this one, and it is the question the document is least equipped to answer. The answer depends entirely on things printed nowhere on it.

Everything on the left is on the paper. Nothing on the right is. NO RATE, LIMIT, TERM, CONDITION OR TAX TREATMENT IS STATED ON EITHER SIDE OF THIS DRAWING. WHAT THIS DOCUMENT ANSWERS What the year started from What went in, and on exactly which date What the credit for the year came to What the account holds once it lands Whether the whole thing reconciles ALL OF IT CHECKABLE FROM THE PAPER ITSELF, WITH NOTHING TAKEN ON TRUST. WHAT IT DOES NOT ANSWER What next year's credit will be What rate will apply to any future year Whether this is where the money belongs What the balance will buy in future Whether the household is doing enough NONE OF IT IS ON THE PAPER, AND NONE OF IT CAN BE GOT FROM THE PAPER. A STATEMENT RECORDS. IT DOES NOT DECIDE, AND IT DOES NOT PREDICT. Both lists describe an invented statement drawn for teaching.
The left column is everything the paper settles and the right column is everything a household still has to decide, and no amount of reconciling moves an item across.

None of that is a criticism of the document. Silence on that question is the whole point. A record that tried to answer whether a household is doing enough would have to make assumptions about that household's life, and would stop being a record. The statement offers four solid facts and a reconciliation instead, and that is more than most paper a household receives offers.

Try it out

Name something this statement genuinely cannot say.

How this gets used

What other people do with the very same document

Somebody assessing a household for a loan may ask to see a document like this one, and will read it for something the household is not reading it for. Twelve dated deposits in twelve months, made by a household rather than deducted by an employer, is a record of a habit, and a record built by a third party is harder to arrange than a letter. Each lender's own policy decides what it does with what it sees.

A clerk at a counter reads it differently again, and reads almost nothing of it. Identity block, closing balance, and whether the year covered is the year being asked about. Everything this guide has spent thousands of words on is, to somebody processing a request, three lines near the top and one near the bottom. At that counter, the document is for those four lines and nothing more.

The household's own use is the narrowest of the three and the only one that changes anything the household controls: the sheet it keeps for itself now says Rs 89,489/- where it used to say Rs 84,000/-, and it says it for a reason the household can explain. A sheet the household can explain is the whole practical gain. Reading the document changes what the household knows and nothing else, so no outcome is promised and none is available to promise.

For Ashok Bhosale none of it applies at all. A tailoring counter produces no statement of any kind, so there is nothing to reconcile. A household in that position that wants what this document gives has to build it: a ruled notebook with a date and an amount on every line, the same four columns without the printing. A notebook is more work and it is not less respectable.

Set out elsewhere. The public provident fund itself is covered separately. No interest rate is stated: the 7 per cent a year and the 0.5833 per cent a month used throughout are assumptions, labelled as such at every appearance. The deposit limit for a year, the term, the lock-in period, the withdrawal conditions, the loan conditions and the tax treatment are all set by rules that change: the Ministry of Finance sets the small savings arrangements and the Reserve Bank of India publishes at rbi.org.in, and where tax is concerned the Central Board of Direct Taxes publishes at incometaxindia.gov.in. Each is worth confirming at source. Whether a household should deposit more, or less, or at all is the household's own question, as is whether to reorganise a month around the fifth. No bank, no provider and no product is named.

Value at Risk and What It Hides teaches you to compute value at risk three ways, interpret the figure, and say precisely what it refuses to describe.

References

SourceDocumentWhere
Ministry of FinanceThe framework under which the small savings arrangements sit, including the account read here: the rate declared on balances, the amounts allowed in a year, the term, and the circumstances in which anything may be taken out. Named for the existence of that framework onlyrbi.org.in
Reserve Bank of IndiaPublished material on the small savings arrangements and on account statements as records issued to the person an account belongs to. Named for the fact that the current terms are published rather than rememberedrbi.org.in
Central Board of Direct TaxesPublished material on how an arrangement of this kind is treated for tax, the place where the tax treatment is set outincometaxindia.gov.in
Employees' Provident Fund OrganisationPublished material on the employer provident fund arrangement, named only to mark that it is a different arrangement and is not the document read hereepfindia.gov.in
Pension Fund Regulatory and Development AuthorityPublished material on the National Pension System, which is a separate arrangement and is not the document being read herepfrda.org.in

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.

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