Foundation — Case 1 worked in full, and the Excel functions the examination expects

A man climbs an escalator that is moving downwards. He climbs eleven steps a minute; the escalator carries him down ten. His real progress is one step a minute, not eleven.

That is the inflation-adjusted return, and the workbook computes it exactly that way: =((1+11%)/(1+10%))−1 = 0.91%.

Notice it is not 11 − 10 = 1 per cent. The division matters, and at higher rates the difference grows. Case 4 uses 8 per cent against 6 per cent and gets 1.89 per cent, not 2. Practice Question 3 uses 10 against 6 and gets 3.77 per cent, not 4. Practice Question 9 uses 9 against 8 and gets 0.93 per cent, not 1.

Why it is used. Retirement withdrawals do not stay flat — they rise every year with inflation. Discounting a rising stream at the plain return would pretend the withdrawals stay level, and would understate the corpus required, sometimes enormously.

See how enormously. Mr Z needs Rs 1,44,96,632 for 15 years of rising withdrawals of Rs 10,28,923. Discounted at the plain 11 per cent, the same 15 payments would come to roughly Rs 76 lakh. The difference is almost the whole answer — and a candidate who forgets the adjustment does not get a slightly wrong figure, they get a completely wrong one.

The one step a minute is what actually gets him to the top. The eleven steps are an illusion created by ignoring the escalator.

Mr Z contributes Rs 9,000 a month, and it rises 20 per cent every year. Most people, asked to estimate eight years of that, multiply Rs 1,08,000 by eight and get about Rs 8.6 lakh.

The actual total contributed is Rs 20,38,282, and grown at 8 per cent it becomes Rs 26,44,798 — more than three times the naive estimate.

The workbook does it one row at a time, and that is the right method because each year's contribution has a different amount AND a different number of years to grow:

Rs 1,29,600 at age 53 has 7 years to grow. Rs 4,64,380 at age 60 has none.

Note the shape of this, because it is counter-intuitive. The biggest contributions get the least compounding, and the smallest get the most. At age 53 he puts in Rs 1,29,600 and it becomes Rs 2,22,112 — a gain of 71 per cent. At age 60 he puts in Rs 4,64,380 and it stays Rs 4,64,380.

Which is exactly why the existing Rs 12,00,000 matters so much. It is one number, contributed before the exercise even starts, and it grows to Rs 22,21,116 — 46 per cent of the entire retirement corpus. Eight years of rising contributions produce Rs 26.4 lakh; twelve lakh sitting there for eight years produces Rs 22.2 lakh.

The lesson an adviser takes from the table is not about Mr Z. It is that money already invested is doing more work than money about to be invested — which is the strongest possible argument against Anjali's eleven months of closing the laptop in Chapter 17.

A tenant and a landlord agree on Rs 30,000 a month for two years. Then they argue about whether it is payable on the first of the month or the last.

It is the same rent and it is not the same money. Twenty-four payments starting today are worth more than twenty-four starting a month from now, by exactly one month of interest on the whole stream.

Excel handles this with a fifth argument. PV(rate, nper, pmt, fv, 1) — and the workbook explains it in its own note: 1 denotes payment at the beginning of the period.

Case 1 uses it. Mr Z needs his first year's expenses on the day he retires, so the workbook writes =PV(0.91%, 15, −1028922.63, , 1) and gets Rs 1,44,96,632.

Practice Question 9 does not use it. Jaspreet's corpus is computed as =PV(0.93%, 25, −2796574.29) with no trailing 1, giving Rs 6,21,56,919.

Case 4 uses it too, and says so explicitly: the couple's expenditure arises at the beginning of each year.

So the examination is testing whether you read the question, not whether you know the function. Look for the words. "Received yearly in advance", "at the beginning of each year", "expenses on the day he retires" — all mean the trailing 1. "At the end of each year" — as in Mr Y's son's fees — means leaving it out.

On Mr Z's numbers the trailing 1 is worth about Rs 1.3 lakh. Not enough to be obvious, and quite enough to send you to the wrong option.

Mr Smart retires with a pension of Rs 4,80,000 that adjusts partially with inflation to the extent of 50 per cent. It sounds protective. It is an umbrella with holes in it, and the holes get larger every year.

His expenses rise at 6 per cent. His pension rises at 3 per cent. The gap in year one is small — about Rs 14,400 — and easy to dismiss.

By year fifteen the pension has grown to about Rs 7.48 lakh and the expenses to about Rs 11.50 lakh. The gap is over Rs 4 lakh a year. By year twenty-seven the gap is larger than the original pension.

That is why the workbook's answer to Case 4 question 1 is Rs 80,18,710 — the present value, at 5 per cent, of 28 years of that widening gap plus Rs 1,00,000 a year of social and travel expenses inflating at 6 per cent, all payable at the beginning of each year.

And the couple has Rs 40 lakh.

The workbook does not conclude that they are ruined. It asks a better question, in sub-question 2: at what return does Rs 40 lakh actually fund the requirement? The answer is 9.90 per cent per annum — which reframes an alarming shortfall into a clear, testable investment objective.

That reframing is the professional skill this chapter is teaching. A shortfall stated as "you need Rs 80 lakh and you have Rs 40 lakh" invites panic. Stated as "your corpus must earn 9.90 per cent" it invites a conversation about what is achievable — and, given Chapter 18, about whether 9.90 per cent is compatible with what a 60-year-old couple can bear.

Two families buy what sounds like the same thing: a small base health policy and a large cheap policy sitting above it. One family ends the year paying Rs 6 lakh from their own pocket and the other pays nothing.

The workbook sets them side by side in Practice Questions 5 and 6, with identical claims of Rs 2 lakh, Rs 3 lakh and Rs 4 lakh in one year.

Esther has a TOP-UP — Rs 10 lakh cover with a Rs 5 lakh deductible. A top-up applies its deductible to each single claim. No individual claim reaches Rs 5 lakh, so the top-up never activates at all. Her Rs 3 lakh base policy absorbs what it can — Rs 2 lakh, then Rs 1 lakh, then nothing — and she pays Rs 6 lakh herself. She owns a Rs 10 lakh policy that paid nothing in a year of Rs 9 lakh of claims.

Fahad has a SUPER TOP-UP — Rs 10 lakh with a Rs 3 lakh deductible. A super top-up applies its deductible to the aggregate of claims in the year. His base policy pays Rs 2 lakh and then Rs 1 lakh, and in doing so the Rs 3 lakh deductible has been met over the two medical incidences. The super top-up then pays Rs 2 lakh on the second claim and Rs 4 lakh on the third. He pays NIL.

The difference is not the sum insured, and it is not really the deductible amount either. It is the word AGGREGATE.

This is the most practically valuable distinction in the whole practice set, because both products are sold as inexpensive ways to raise cover, and a family with several moderate claims in one year gets nothing from a top-up and everything from a super top-up.

A trader has Rs 25,000 of his own. He borrows Rs 35,000 at 9 per cent and puts the whole Rs 60,000 into something yielding 10 per cent.

The asset earns Rs 6,000. The loan costs Rs 3,150. He keeps Rs 2,850 — on his own Rs 25,000, that is 11.4 per cent.

That is Ms T in module-end question 3, and the arithmetic rewards care. Leverage of 1.4 times means the borrowing is 1.4 times her own funds, so own + 1.4 × own = 2.4 × own = Rs 60,000, giving own funds of Rs 25,000 and borrowing of Rs 35,000.

Why the return on equity rose from 10 per cent to 11.4 per cent. She borrowed at 9 and earned 10 on the borrowed money, keeping the 1 per cent spread — Rs 350 on Rs 35,000 — and that Rs 350 is added to the Rs 2,500 her own money earned. Rs 2,850 on Rs 25,000 is 11.4 per cent.

Now turn the asset down. Suppose it yields 5 per cent instead of 10. The asset earns Rs 3,000, the loan still costs Rs 3,150, and she is down Rs 150 — a negative return on her own money, from an asset that made a positive 5 per cent.

Leverage did not make the investment better. It made the outcome bigger in both directions, and the borrowing cost of 9 per cent is fixed whichever way the asset moves. An investor who understands only the 11.4 per cent has seen one half of a symmetrical device.

A man holds a confirmed ticket for next Tuesday's train and tries to board today, arguing that the ticket is genuine and registered.

It is genuine. The train is not here.

Practice Question 10 turns on exactly this. L has made a registered Will leaving her house to her son. Her son wants a loan against the house, showing the Will to prove his future ownership.

The answer is (d) — No, since the provisions of the Will apply only on L's demise, and the workbook's hint puts it plainly: a Will comes into effect only on death and can be changed by her before her death.

Both halves of that hint matter. It has no effect yet, and she can change it tomorrow. Registration does not freeze it — the son has no present interest of any kind, and nothing to offer as security.

The third sub-question makes the same point from the other side, and shows the practical way out. L's daughter needs money urgently, and the mutual funds are willed to her. A copy of the Will is no help. Making her a joint holder is not the answer either. The workbook's solution is (c): L can make a gift to her daughter of the required sum of money, with the hint: as the primary holder of the mutual fund, L has to redeem the mutual fund investment. This can be gifted to her daughter for her immediate use and it is also TAX FREE.

The living owner acts; the Will waits. And a gift from a mother to a daughter is exempt, since she is a relative under the gift provisions — which is the Chapter 9 material arriving exactly where it is needed.

People ask "how much life insurance should I have?" as though the answer were a property of the person. It is not. It is a property of what stops when they do.

The practice cases show two clean methods and they answer different questions.

Adil's case is a needs analysis. What must the money do? Provide Rs 3,00,000 a year of household expenses for 30 years — which at an inflation-adjusted return of 1.89 per cent needs Rs 68,24,712. Repay a home loan of Rs 30,00,000. Leave a child's corpus of Rs 10,00,000. Total Rs 1,08,24,712, less existing cover of Rs 50,00,000, leaves Rs 58,24,712 — about Rs 58 lakh.

Charu's case is an income replacement. What would have been earned? Rs 6,00,000 a year for the 25 working years remaining, at an inflation-adjusted return of 3.77 per cent, is Rs 96,01,652. Less her Rs 40,00,000 of cover, she needs Rs 56,01,652 — about Rs 56 lakh.

Note what neither method does. Neither multiplies salary by a fixed number, and neither asks what premium is affordable or what fits the 80C limit.

And note how large both answers are. Charu earns Rs 50,000 a month and needs roughly Rs 96 lakh of total cover — sixteen times her annual income. Chapter 17's complaint that Indians buy completely inadequate insurance because they buy it for tax saving alone is not rhetoric; it is what these two calculations demonstrate.