Private Wealth Management puzzles, solved step by step

Puzzles: 100
Traced to a firm: 3
Topics: 13
Hard: 30

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053At 9% a year, roughly how long does Rs 10 lakh take to become Rs 80 lakh? Answer in your head, then check it.Compounding and doublingWarm upIndian wealth management
Try it first
Your first answer, inside ten seconds?
Show the worked solution
About 24 years. Rs 10 lakh to Rs 80 lakh is eight times the money, which is three doublings. At 9% the rule of 72 gives 72 / 9 = 8 years per doubling, so three doublings take about 24 years. The exact figure, the log of 8 over the log of 1.09, is 24.13 years, so the shortcut is off by under two months.
Why count doublings instead of years?
A staircase is easier to climb in your head than a ramp. Compound growth is a ramp, but every doubling takes the same number of years at a fixed rate, so you can turn it into equal steps. First ask how many times the money must double, then multiply by the years one doubling takes. Eight times is 2 x 2 x 2, three doublings, and at 9% each takes about 8 years.
At 9% a year Rs 10 lakh reaches Rs 20 lakh in about 8 years, Rs 40 lakh in about 16 and Rs 80 lakh in about 24, because every doubling takes the same time; the exact path reaches Rs 80 lakh in 24.1 years.
How good is the rule of 72 at 9%?
Very good. The exact doubling time at 9% is the log of 2 over the log of 1.09, which is 8.04 years, against 8.00 from the rule. The rule of 72 is most accurate for rates around 8%, which is why it serves so well for Indian savings and equity assumptions. Three doublings carry the small error three times, which is how 24 becomes 24.13.
The relationship
$t = \frac{\ln 8}{\ln 1.09} = \frac{2.079}{0.0862} \approx 24.13\ \text{years}$
8 the growth multiple needed, 80 lakh over 10 lakh
1.09 one year of growth at 9%
t years needed
What it says in wordsThe years needed are the log of the multiple divided by the log of one year's growth.
Then turn it into a client sentence. Rs 10 lakh at 9% needs a working lifetime, not a decade, to reach Rs 80 lakh, and the last doubling, from Rs 40 lakh to Rs 80 lakh, adds more rupees than the first two combined. That is the argument for starting early, said with numbers rather than slogans.
Where candidates lose it
Candidates divide 80 by 10, get 8, and then try to compound year by year in their head. They lose the room in arithmetic. The move is to see that 8 is 2 cubed before touching the rate.
The second slip is quoting 8 years, which is the time for one doubling, because the rule of 72 is the first thing that comes to mind. Say how many doublings first, then the time for each.
What the interviewer asks next
How long does the same money take to reach Rs 1 crore?
At 12% instead of 9%, how many years does the client save on the way to Rs 80 lakh?
Why is the rule of 72 less accurate at 20% a year?
054A client invested Rs 1 lakh six months ago and it is now worth Rs 1.1 lakh. He says that is a 20% annual return. What is the correct annualised figure, and why is annualising six months risky?Returns arithmeticWarm upMutual fund distributionIndian wealth management
Try it first
What is 10% in six months, annualised?
Show the worked solution
Annualised, 10% in six months is 21%, not 20%, and neither is a return he has earned. Repeating 10% on the larger Rs 1.1 lakh base gives Rs 1.21 lakh in a year. But annualising assumes the next six months repeat the last six. If they give back 10% instead, the year ends at Rs 99,000, a 1% loss. Short windows are mostly noise.
Why is it 21% and not 20%?
A cricketer who scores 50 in the first ten overs is not guaranteed 250 in fifty, and even the projection has to use the right arithmetic. Annualising a half-year return means compounding it, because the second half would grow the bigger balance. Rs 1 lakh becomes Rs 1.1 lakh, and another 10% on Rs 1.1 lakh is Rs 11,000, not Rs 10,000, which is where the extra point comes from.
The relationship
$r_{\text{annual}} = (1 + r_{\text{half}})^2 - 1 = 1.10^2 - 1 = 21\%$
r_half the return over six months, 10%
2 the number of six-month periods in a year
What it says in wordsCompound the period return as many times as the period fits into a year, then subtract one.
Ten per cent in six months annualises to 21% because the second half compounds on Rs 1.1 lakh, but the year can still end anywhere from plus 21% to minus 1% depending on the next six months, so an annualised short return is a projection, not a result.
Why is annualising a short window risky?
Annualising quietly assumes the next six months will look like the last six. Over short windows, most of a fund's return is noise, and scaling noise up to a year makes it look like a trend. Look at the bottom of the figure: the same first half ends the year at plus 21%, plus 10% or minus 1%, depending on a second half nobody has seen. This is why fund documents commonly show returns for periods under a year as absolute figures rather than annualised ones; confirm the current SEBI presentation rules before you quote them.
In the room, give both halves of the answer: the corrected 21%, then the caution. A client who hears 21% a year will plan around it. A client who hears 10% so far, which would be 21% if it repeated, which it may not, has the number and its limits.
Where candidates lose it
The trap has two layers. The first is agreeing with 20%, doubling instead of compounding. It is a small error, but it tells the interviewer you add returns that should be multiplied.
The larger miss is stopping at 21%. The question asks why annualising is risky, and a candidate who does not say it projects noise has answered only the arithmetic half.
What the interviewer asks next
A fund made 3% in one month. What is that annualised, and would you ever quote it?
The client's Rs 1.1 lakh drops to Rs 1 lakh over the next six months. What was his return for the year?
Why do fund documents usually show returns under a year as absolute numbers?
055Rs 50 lakh sits in the regular plan of a mutual fund, which charges 0.8% a year more than the direct plan of the same fund. If the direct plan compounds at 11% a year after its own costs, what is the gap in ending wealth after 20 years?Fee and cost dragWarm upMutual fund distributionIndian wealth management
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Roughly how large is the gap after 20 years?
Show the worked solution
About Rs 54 lakh. At 11% the direct plan grows Rs 50 lakh to about Rs 403.1 lakh in 20 years. At 10.2% the regular plan reaches about Rs 348.8 lakh. The gap is Rs 54.3 lakh, 13.5% of the direct plan's ending value, from a cost difference that sounds like less than one per cent.
Why is the gap so much larger than 0.8% sounds?
A slow leak in a water tank loses a little each hour, but it keeps leaking from a tank that is also being filled, and every litre lost is a litre that never reaches the tap. An annual fee is charged on the whole growing balance every year, and each rupee taken stops compounding for the rest of the period. Charged only on the starting Rs 50 lakh, 0.8% for 20 years would be Rs 8 lakh. Charged on a balance that grows several times over, it is Rs 54 lakh.
Rs 50 lakh in the direct plan at 11% and the regular plan at 10.2% ends Rs 3.0 lakh apart after 5 years, Rs 9.9 lakh after 10 and Rs 54.3 lakh after 20, because the fee gap compounds along with the money.
How do you estimate it without a calculator?
Use the ratio of the two growth factors. Each year the regular plan keeps 1.102 / 1.11 of what the direct plan keeps, about 0.9928, so it loses roughly 0.72% of the direct plan's value a year. Over 20 years that compounds to about 1 minus 0.9928 to the 20th, roughly 13.5% of the ending value. The direct plan ends near Rs 400 lakh, so the gap is a little over Rs 50 lakh. Two lines of arithmetic, and the answer is within a lakh or two.
The relationship
$\text{gap} = 50\,(1.11^{20} - 1.102^{20}) \approx 54.3\ \text{lakh}$
50 the investment, Rs lakh
1.11 one year of growth in the direct plan
1.102 one year of growth in the regular plan, 0.8% lower
What it says in wordsThe gap is the same money compounded at two rates for 20 years, subtracted.
Be fair to the regular plan when you say this to a client. The extra cost pays the distributor, and some investors value the advice and service they get for it. The numeracy point is only that the price of that service, over 20 years, is measured in tens of lakhs, and the client should see it in rupees before deciding.
Where candidates lose it
The fast wrong answer is 0.8% x Rs 50 lakh x 20 years, Rs 8 lakh. It charges the fee only on the starting amount and ignores that each rupee of fee also loses its future growth.
The second miss is presenting the gap as proof that one plan is bad. The interviewer wants the number and a fair sentence on what the extra cost buys.
What the interviewer asks next
What share of the ending value is lost if the gap is 1.5% a year instead of 0.8%?
How does the answer change for a monthly SIP of Rs 50,000 instead of a lump sum?
What would a client get for the extra cost in a regular plan, and how would you judge whether it is worth it?
058A fund has not had a single losing year in seven years, and the salesperson presents that as proof it is safe. If any given year had a 30% chance of a loss, how likely was a clean seven-year record anyway?Probability and risk of lossWarm upMutual fund distributionIndian wealth management
Try it first
Your estimate of the chance of seven clean years?
Show the worked solution
About 8%, which is unusual but not rare. A clean year has probability 0.7, and seven independent clean years is 0.7 to the 7th, 0.082. Among 100 funds carrying the same 30% yearly chance of a loss, about eight would show a clean seven-year record by luck. The record makes a safer fund more likely, but it does not prove the fund is safe.
How do you get to 8% in your head?
Square, then keep multiplying. 0.7 x 0.7 is 0.49, call it a half. Two more years take it to about a quarter, 0.24, two more to about an eighth, 0.12, and the seventh year times 0.7 gives about 0.08. Each extra clean year multiplies the chance by 0.7, so the probability of an unbroken run falls away quickly but never reaches zero. It is the same arithmetic as a batsman who survives each over with probability 0.7 lasting seven overs.
If each year carries a 30% chance of a loss, the chance of no losing year falls from 70% after one year to 49% after two and to 8.2% after seven, so about 8 funds in 100 would show a clean seven-year record by luck alone.
So is the record evidence of anything?
Yes, but weigh it properly. Compare with a fund that truly has only a 10% chance of a losing year: it keeps a clean seven-year record 0.9 to the 7th of the time, 47.8%. A clean record is about 5.8 times more likely from the safer fund than from the riskier one, which shifts the odds but does not settle them. With hundreds of funds on sale, some risky ones will carry spotless records, and those are exactly the ones placed in front of clients.
There is a second problem the arithmetic hides. Years are not independent across funds: in a strong market decade most funds have no losing years at the same time, so seven clean years may say more about the decade than about the fund. Ask how the fund behaved in the worst year the market had, not how many years it avoided a loss.
Where candidates lose it
The trap is hearing seven out of seven and treating it as near-certain proof. Candidates rarely compute the chance of the record under the risky assumption, so they cannot say how surprising it really is.
The opposite miss is dismissing the record as pure luck. It is evidence; the good answer quantifies how much, then names what it cannot show.
What the interviewer asks next
How many clean years would you need before the chance under a 30% loss rate falls below 1%?
If 200 funds each have a 30% yearly loss chance, how many clean seven-year records do you expect?
Why might a clean record in a rising market be weaker evidence than one that spans a crash?
059A client spends Rs 1 lakh a month and holds Rs 2.4 crore of investments. How many years of spending is that, and how far is it from the common planning marker of 25 times annual spending?Retirement and withdrawalWarm upIndian wealth management
Try it first
Rs 2.4 crore against Rs 1 lakh a month is how many years of spending?
Show the worked solution
Twenty years of spending, Rs 60 lakh short of 25 times. Rs 1 lakh a month is Rs 12 lakh a year, and Rs 2.4 crore over Rs 12 lakh is 20. Twenty-five times spending would be Rs 3 crore. Put another way, the client would withdraw 5% of the corpus in year one, against the 4% that the 25 times marker implies.
Why express a corpus in years of spending?
A client hears Rs 2.4 crore and feels rich; a client who hears twenty years of your current life hears a question: and after that? Dividing the corpus by annual spending turns an abstract balance into a length of time, which is what a retirement decision is actually about. It also removes the units: the same arithmetic works for a Rs 50 lakh corpus or a Rs 50 crore one.
Rs 2.4 crore is 20 blocks of Rs 12 lakh, twenty years of spending, and the 25 times marker sits at Rs 3 crore, so the client is Rs 60 lakh short and would withdraw 5% a year rather than 4%.
Where does 25 times come from, and how firm is it?
Twenty-five times spending is the same thing as withdrawing 4% a year, the 4% ruleA planning guideline from US research by William Bengen in the 1990s: withdraw 4% of the starting portfolio, raised each year for inflation, and the money historically lasted about 30 years. from US retirement research. It is a starting point, not a law, because it came from one country's market history and a 30 year retirement. Higher inflation, longer lives and early retirement all argue for a larger multiple, and planners in India often use one. Say the marker, then say its limits.
Does twenty years of spending mean the money runs out in twenty years?
Only if the corpus earns exactly inflation. If it earns 2% a year above inflation and the client withdraws Rs 12 lakh in today's money at the start of each year, the money lasts about 25 years. Years of spending is a zero-real-return yardstick, so it is conservative when real returns are positive and optimistic when they are negative. That is why it is the right first number to say, and the wrong last one.
Where candidates lose it
The arithmetic trap is dividing by the monthly figure, or mixing lakh and crore, and announcing 240 or 2.4 years. Convert both numbers to lakh a year before dividing.
The judgement trap is treating 25 times as a pass mark. A good answer gives the gap, Rs 60 lakh, and then says the marker came from one market's history and needs adjusting for this client.
What the interviewer asks next
How much would the client have to cut monthly spending to reach 25 times today?
If the corpus earns 1% above inflation, how long does Rs 2.4 crore last?
Why might a 45 year old retiring early need more than 25 times?
077A client tells you his Rs 5 lakh investment became Rs 20 lakh in 12 years. Without a calculator, what annual growth rate is that?Compounding and doublingWarm upWealth management
Try it first
Your instinct, in five seconds.
Show the worked solution
About 12% a year. Rs 5 lakh to Rs 20 lakh is four times, which is two doublings. Two doublings in 12 years means one every 6 years, and the rule of 72 gives 72 divided by 6, which is 12%. The exact rate is 4 to the power one twelfth, less 1, which is 12.25%.
Why turn the multiple into doublings first?
If someone tells you a town's population went from 5,000 to 20,000, you naturally say it doubled and doubled again. Doublings are easy to count and hard to get wrong. A growth multiple that is a power of two converts straight into a number of doublings, and the rule of 72 turns years per doubling into a rate. Four times is two doublings; eight times would be three.
Rs 5 lakh doubles to Rs 10 lakh in six years and doubles again to Rs 20 lakh by year 12, so the rule of 72 gives 72 / 6 = 12% a year against an exact 12.25%.
How good is the rule of 72 here, and when does it slip?
The relationship
$r = 4^{1/12} - 1 = 12.25\% \qquad \text{rule of 72: } 72/6 = 12\%$
4 the multiple, Rs 20 lakh over Rs 5 lakh
1/12 one twelfth, because the growth happened over 12 years
r the compound annual growth rate
What it says in wordsThe exact rate is the twelfth root of the multiple, less one; the rule of 72 gets within a quarter of a point.
The rule of 72 is most accurate for rates around 8%, and it drifts at the edges: at 12% it undershoots slightly, and at 20% or more it undershoots by more. For interview purposes, 12% with the words "a shade over" is the answer that shows you know it is an approximation. If the multiple is not a clean power of two, say 5 times in 12 years, estimate the doublings: 5 is a bit over two doublings, about 2.3, so a doubling every 5.2 years and roughly 14%.
Then turn it back to the client. A 12% compound rate over 12 years is a good result, but ask what it was in and what the fees and taxes were, because the client quoted a pre-tax figure from memory.
Where candidates lose it
The fast wrong answer is 25%: a 300% gain split evenly over 12 years. It treats the growth as a straight line and overstates the rate by more than double.
The second slip is reaching for a calculator or saying "about 10%" without a method. Say two doublings, six years each, 72 over 6: the method is what the interviewer is listening for.
What the interviewer asks next
The same Rs 5 lakh became Rs 40 lakh in 18 years. What rate is that?
At 12%, how long does it take Rs 20 lakh to reach Rs 1 crore?
The client says 12% beat the market. What do you ask him next?
079An equity fund keeps 10% of its money in cash, earning 6%, while the stocks it holds return 14%. How much does the cash cost the fund's return each year?Fee and cost dragWarm upMutual fund distributionIndian wealth management
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How much return does the cash cost?
Show the worked solution
About 0.8 of a point a year. The fund earns 90% x 14% plus 10% x 6%, which is 12.6 plus 0.6, or 13.2%. Fully invested it would earn 14%. The drag is the cash weight times the gap in returns: 10% x (14 - 6) = 0.8 of a point, in a year when stocks beat cash.
Where does the 0.8 of a point come from?
Picture a shop with ten shelves, nine stocked with goods that earn a good margin and one kept empty as a buffer for a delivery that may come. The empty shelf is not free: it costs the margin it would have earned. Cash drag is the cash weight times the gap between what cash earns and what the invested money earns. Here that is 10% times 8 points, or 0.8 of a point.
Stocks at 90% of the fund earning 14% contribute 12.6 points and cash at 10% earning 6% contributes 0.6, a blended 13.2% that is 0.8 of a point below the 14% a fully invested fund would earn.
The relationship
$\text{drag} = w_{cash} \times (r_{stocks} - r_{cash}) = 0.10 \times (14\% - 6\%) = 0.8\%$
w_cash the share of the fund held in cash, 10%
r_stocks the return on the invested stocks, 14%
r_cash the return on cash, 6%
What it says in wordsThe cost of idle cash is its weight times the return it gives up.
Is the cash ever worth it?
Yes, and say so. In a year when stocks fall 10%, the same fund loses 8.4% rather than 10%, so the cash cushions. It also pays redemptions without forcing the manager to sell into a falling market. Cash drag is a cost in rising markets and a cushion in falling ones, so the question for a client is whether the manager holds cash on purpose or by accident. A fund that is always 10% in cash is charging an equity fee on money sitting in a deposit.
Scale it up to show the stakes: 0.8 of a point a year compounds. Rs 1 crore at 14% for ten years grows to about Rs 3.71 crore; at 13.2% it grows to about Rs 3.45 crore.
Where candidates lose it
Candidates often answer 0.6 of a point, confusing what the cash earns with what it costs, or 1.4 points, a tenth of the stock return, forgetting the cash still earns something.
The other loss is calling cash pure waste. Say the drag, then say the cushion in a falling year: the interviewer wants to hear that you see both sides of the same holding.
What the interviewer asks next
Stocks return minus 10% this year. What does the fund return?
At what stock return does the cash stop being a drag?
How would you check whether a fund's cash level is deliberate?
084A bank fixed deposit quotes 7% a year, compounded quarterly. What is the effective annual yield?Fixed income numeracyWarm upIndian wealth management
Try it first
Pick the effective yield.
Show the worked solution
About 7.19%. Quarterly compounding pays 7 / 4 = 1.75% each quarter, and each quarter's interest earns interest in the quarters that follow. Rs 100 grows to 101.75, 103.53, 105.34 and 107.19. The effective yield is 1.0175 to the fourth, less 1, which is 7.19%.
Why is the effective yield above the quoted 7%?
If a friend repays you in four instalments and you lend each instalment on at once, you end the year with more than if the whole amount came back at year end. The quoted rate is the per-period rate times the number of periods; the effective yield adds the interest earned on interest paid earlier in the year. The more often it compounds, the wider the gap.
Rs 100 grows by 1.75% a quarter to Rs 107.19 at the year end, each quarter's interest slightly larger than the last, so the effective yield is 7.19% against the quoted 7%.
The relationship
$\text{EAR} = \left(1 + \frac{0.07}{4}\right)^4 - 1 = 1.0175^4 - 1 = 7.19\%$
0.07 the quoted annual rate
4 compounding periods a year
EAR the effective annual rate, what Rs 100 actually becomes in a year
What it says in wordsDivide the quoted rate by the periods, compound it that many times, and subtract one.
When does the 7.19% not apply?
The effective yield assumes the interest stays in the deposit; on a payout deposit that sends interest to the client each quarter, he earns 7% unless he reinvests it himself. Tax is the second gap: interest on deposits is typically taxed as income each year at the client's slab rate, so the after-tax figure is lower still. Confirm the current treatment before comparing a deposit with a fund.
Use the effective rate whenever you compare products that compound at different frequencies, such as a quarterly deposit against an annual-coupon bond. Comparing quoted rates across frequencies is comparing different units.
Where candidates lose it
The common slip is to say 7% because that is what the bank quoted. The interviewer is checking whether you hear the words "compounded quarterly" and know they change the answer.
The rarer slip is reading 7% as a quarterly rate and quoting about 31%. Say the per-quarter rate, 1.75%, out loud before compounding.
What the interviewer asks next
What would the effective yield be with monthly compounding?
A bond pays 7.1% once a year. Which pays more, the bond or the deposit?
How does a 30% tax slab change the comparison?
085A client bought a stock at Rs 500 and it now trades at Rs 300. He says he will sell only once it gets back to Rs 500. What return does he need just to get there, and what is wrong with the plan?Behavioural trapsWarm upWealth management
Try it first
What rise takes Rs 300 back to Rs 500?
Show the worked solution
He needs 66.7%, and the plan anchors on a price the market does not care about. Getting from Rs 300 to Rs 500 is a rise of 200 on 300. At 12% a year that is about 4.5 years. The purchase price is history; the question is whether he would buy the stock at Rs 300 today.
Why is 66.7% bigger than the 40% he lost?
A shirt marked down from Rs 500 to Rs 300 is 40% off. Marking it back up to Rs 500 is a 66.7% rise, because the markup is taken on the lower price. A percentage recovery is measured from the lower base, so the gain needed to recover always exceeds the loss suffered.
The relationship
$g = \frac{500}{300} - 1 = 66.7\% \qquad n = \frac{\ln(5/3)}{\ln 1.12} \approx 4.5 \text{ years}$
g the rise needed to get back to the purchase price
n years to get there at 12% a year
What it says in wordsThe rise needed is the purchase price over today's price, less one; at 12% a year it takes about four and a half years.
The Rs 500 purchase price sits above today's Rs 300 like an anchor, and reaching it needs a 66.7% rise, about 4.5 years at 12% a year, although the market sets no target from what the client paid.
What is wrong with waiting to get back to Rs 500?
AnchoringLeaning on a reference number, here the purchase price, when judging a value that should not depend on it. on the purchase price makes a past number decide a future choice. The stock's next return is the same whether he bought at Rs 500 or Rs 200, so the only live question is whether Rs 300 of this stock is the best use of Rs 300 today. Holding a loser to avoid admitting a loss, while selling winners early, is a well documented pattern called the disposition effect.
Say it kindly. Nobody enjoys booking a loss, and the job is not to tell the client he was wrong. Ask him whether he would buy it today at 300; if the answer is no, he is holding it only because of a number from the past. A booked loss may also offset other gains for tax, which is a real reason to act rather than wait.
Where candidates lose it
The fast wrong answer is 40%, the size of the fall. It measures the recovery on the old base, and the interviewer hears that you would not spot the same error in a client's thinking.
The bigger loss is doing only the arithmetic. The question asks what is wrong with the plan: name anchoring, give the one question that breaks it, and say it without making the client feel foolish.
What the interviewer asks next
The stock falls further to Rs 250. What rise is needed now?
Why do investors tend to sell winners too early and hold losers too long?
How would you raise this with a client who is emotionally attached to the stock?
089A relationship manager's book grew from Rs 400 crore to Rs 500 crore over a year in which his clients' portfolios rose 12%. How much net new money did he bring in?Wealth business economicsWarm upWealth management
Try it first
How much of the Rs 100 crore growth is new money?
Show the worked solution
About Rs 52 crore. The market alone would have taken the book from Rs 400 crore to Rs 448 crore, 12% of 400 being Rs 48 crore. The rest of the growth to Rs 500 crore, Rs 52 crore, is net new money: fresh money in less withdrawals. If the new money arrived through the year and earned some of the rise, the figure is nearer Rs 49 crore.
Why separate the market from the money raised?
A shop's sales rise 25% in a year when prices across the market rose 12%. Most of that rise is inflation, not new customers. Assets under management grow from two sources, the market and net new money, and only the second measures what the adviser did. A banker who quotes 25% growth in a year when markets rose 12% is quoting a number he did not earn in full.
The book of Rs 400 crore gains Rs 48 crore from a 12% market and Rs 52 crore of net new money to close at Rs 500 crore, so only about half of the Rs 100 crore growth came from the adviser.
The relationship
$NNM = 500 - 400 \times 1.12 = 500 - 448 = 52$
NNM net new money: new client money in, less money withdrawn
400 x 1.12 where the opening book would be from market moves alone
What it says in wordsNet new money is the closing book less what the opening book would have grown to on its own.
When is Rs 52 crore not quite right?
The simple version assumes the new money arrived at the year end, so it earned nothing. If new money came in steadily, part of the market's rise was earned on it, so the true net new money is a little lower than the simple subtraction. With money arriving evenly and earning about half the year's 12%, it is 52 divided by 1.06, about Rs 49 crore.
Say also what the figure hides: net new money is inflows less outflows, so Rs 52 crore could be Rs 80 crore raised and Rs 28 crore lost to clients who left. A manager asking this question usually wants both halves.
Where candidates lose it
The common slip is calling all Rs 100 crore new money, or taking 12% off the closing figure instead of the opening one. The market acts on money the adviser already had, so the 12% applies to Rs 400 crore.
The second loss is missing the timing caveat. Give 52, then say it is an upper figure if the money arrived through the year.
What the interviewer asks next
The market fell 8% and the book still grew to Rs 420 crore. What was net new money?
Why do wealth firms report net new money separately from assets?
How would you split net new money into new clients and existing clients?

8	the growth multiple needed, 80 lakh over 10 lakh
1.09	one year of growth at 9%
t	years needed

r_half	the return over six months, 10%
2	the number of six-month periods in a year

50	the investment, Rs lakh
1.11	one year of growth in the direct plan
1.102	one year of growth in the regular plan, 0.8% lower

4	the multiple, Rs 20 lakh over Rs 5 lakh
1/12	one twelfth, because the growth happened over 12 years
r	the compound annual growth rate

Try it first

Why count doublings instead of years?

How good is the rule of 72 at 9%?

Where candidates lose it

What the interviewer asks next

Try it first

Why is it 21% and not 20%?

Why is annualising a short window risky?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the gap so much larger than 0.8% sounds?

How do you estimate it without a calculator?

Where candidates lose it

What the interviewer asks next

Try it first

How do you get to 8% in your head?

So is the record evidence of anything?

Where candidates lose it

What the interviewer asks next

Try it first

Why express a corpus in years of spending?

Where does 25 times come from, and how firm is it?

Does twenty years of spending mean the money runs out in twenty years?

Where candidates lose it

What the interviewer asks next

Try it first

Why turn the multiple into doublings first?

How good is the rule of 72 here, and when does it slip?

Where candidates lose it

What the interviewer asks next

Try it first

Where does the 0.8 of a point come from?

Is the cash ever worth it?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the effective yield above the quoted 7%?

When does the 7.19% not apply?

Where candidates lose it

What the interviewer asks next

Try it first

Why is 66.7% bigger than the 40% he lost?

What is wrong with waiting to get back to Rs 500?

Where candidates lose it

What the interviewer asks next

Try it first

Why separate the market from the money raised?

When is Rs 52 crore not quite right?

Where candidates lose it

What the interviewer asks next