Private Wealth Management puzzles, solved step by step

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

Showing 1–10 of 100

001A client's portfolio doubles every 8 years and is worth Rs 16 crore when she turns 64. At what age was it worth Rs 4 crore, and what share of the final Rs 16 crore arrived in the last 8 years alone?Compounding and doublingCoreWealth management
Try it first
Before you count back: what share of the final Rs 16 crore was added between 56 and 64?
Show the worked solution
She had Rs 4 crore at 48, and half the final wealth arrived in the last 8 years. Doubling forward means halving backward: Rs 16 crore at 64, Rs 8 crore at 56, Rs 4 crore at 48. Everything between Rs 8 crore and Rs 16 crore, a full Rs 8 crore, was added after 56. Doubling every 8 years is a return of about 9% a year.
Why count backwards instead of forwards?
Think of a mango tree whose fruit count doubles each season. If you know the count in the last season, the season before is simply half of it; you never need to know how many mangoes it started with. Under steady doubling, each step back in time halves the amount, so the answer needs only the final value and the doubling period. Two steps of 8 years back from 64 is 48, and two halvings of Rs 16 crore is Rs 4 crore.
Doubling every 8 years takes the portfolio from Rs 1 crore at 32 to Rs 16 crore at 64, so it was Rs 4 crore at 48 and Rs 8 crore at 56, and the last 8 years alone added Rs 8 crore, half the final wealth.
What does the share of the last 8 years tell a client?
It tells her where the money in compounding really comes from. In any doubling process the last doubling adds as many rupees as all the earlier ones put together. The rupees added at each step were 1, 2, 4 and 8 crore after the first crore: the last step is bigger than the three before it combined, which add to 7. That is why an interruption late in the plan, a withdrawal at 56 or a panic sale in a bad year, costs far more than the same interruption at 35.
The relationship
$W_{48} = \frac{16}{2^{(64-48)/8}} = \frac{16}{4} = 4 \qquad r = 2^{1/8} - 1 \approx 9.05\%$
W_48 portfolio value at age 48, Rs crore
(64-48)/8 the number of doublings between 48 and 64, here 2
r the yearly return that doubles money in 8 years
What it says in wordsDivide the final value by two once for every doubling period you step back; the rule of 72 gives 72 over 8, about 9% a year.
Check the rate with the rule of 72: 72 divided by 8 is 9, and the exact figure is 9.05% a year. Say both, then say the limitation: real portfolios do not double on a timetable, so the sequence of good and bad years matters as much as the average. The clean doubling is a teaching model, not a forecast for any client.
Where candidates lose it
The common slip is to divide the time evenly and say the portfolio was Rs 4 crore at a quarter of the way along, or that each of the four doublings added a quarter of the wealth. Both treat compounding as a straight line and give an answer that sounds careful but is wrong.
The second loss is answering 48 and stopping. The interviewer wants the client point: half the money came in the last 8 years, which is why staying invested late in the plan matters most.
What the interviewer asks next
At what age was the portfolio Rs 1 crore, and what return does that imply?
If she withdraws Rs 2 crore at 56, what is the portfolio worth at 64?
What if the portfolio doubles every 9 years instead? What is it worth at 64 starting from Rs 4 crore at 48?
002A fund advertisement says the scheme returned 150% over the last 10 years. What annual rate of return is that?Returns arithmeticWarm upMutual fund distributionIndian wealth management
Try it first
Answer before you calculate.
Show the worked solution
About 9.6% a year. A 150% return means Rs 1 became Rs 2.5. The yearly rate is 2.5 to the power one tenth, minus one, which is 9.60%. Dividing 150 by 10 to get 15% ignores compounding: 15% a year for ten years would turn Rs 1 into 4.05, not 2.5.
Why is 15% the wrong annual figure?
Think of a child's height chart. If a child grew 50 centimetres over ten years, you could say 5 centimetres a year, because height adds. Money does not add; it multiplies, and each year's gain earns its own gain the next year. An absolute return over many years must be converted to a compounded yearly rate before it can be compared with anything else. Dividing by the number of years overstates the yearly rate, and the overstatement grows with the length of the period.
Rs 1 lakh growing to Rs 2.5 lakh is the advert's 150%, and built year by year it is about 9.6% a year, each year's bar 1.096 times the last; reading it as 15% a year would imply 4.05 times, not 2.5.
How do you get 9.6% without a calculator?
Use doubling as the anchor. At about 9.6% money doubles in roughly 7.5 years, so in ten years it goes a little past double, which matches 2.5 times. You can also bracket it: 1.10 to the tenth is 2.59, a touch above 2.5, so the answer is a touch below 10%. Saying a bracket out loud, just under 10% because 10% gives 2.59, is as convincing to an interviewer as the exact 9.60%.
The relationship
$r = \left(1 + R\right)^{1/n} - 1 = 2.5^{1/10} - 1 \approx 9.6\%$
R the absolute return over the whole period, here 150% or 1.5
n the number of years, here 10
r the compounded annual rate, often called CAGR
What it says in wordsTurn the total return into a growth multiple, take the n-th root, and subtract one.
Why does a wealth interviewer care? Because a client comparing a 150% ten-year fund with a fixed deposit quoting a yearly rate is comparing two different units. The 9.6% is also before any comparison with a benchmarkThe index or reference portfolio a fund is measured against, so its return can be judged relative to what the market gave., which is the next question worth asking.
Where candidates lose it
Saying 15% is the whole trap, and it comes from treating the advert's number as if it were simple interest. It is the most common error clients themselves make, which is exactly why a wealth desk tests it.
The second loss is getting 9.6% but not being able to say why 15% is wrong. Have the one-line check ready: 15% compounded for ten years is about 4 times, not 2.5.
What the interviewer asks next
The same fund returned 40% in the last three years. What is the annual rate over those three?
What did it return a year over the first seven years?
Why do regulators ask funds to show annualised returns for periods over a year?
003A portfolio earns 10% a year before fees for 30 years. The client pays an annual fee of 1%. Roughly what share of his final wealth does the fee cost him?Fee and cost dragCoreWealth management
Try it first
Pick the share of final wealth the 1% fee takes.
Show the worked solution
About a quarter: 24% of the final wealth. At 10% a year, Rs 1 grows to 17.45 over 30 years. Net of a 1% fee it grows at 9% to 13.27. The gap of 4.18 is 24% of the gross figure. A fee that looks like one tenth of the return costs a quarter of the wealth because every rupee paid misses its future compounding.
Why does a 1% fee cost so much more than 1%?
Picture a small leak in a water tank that is also being filled faster every year. The leak takes a little each day, but the water it takes is water that would have been there to hold more tomorrow. A fee removes not only the rupee paid but everything that rupee would have earned for the rest of the plan. Over 30 years the growth rate falls from 10% to 9%, and the difference between the two compounding paths widens every single year.
Rs 1 grows to 17.4 at 10% a year over 30 years but only to 13.3 at 9% after a 1% fee, so the fee takes 24% of the final wealth, and the gap between the curves widens every year.
How do you estimate the share in your head?
Use the ratio of the two growth factors. Each year the net portfolio is 1.09 over 1.10, about 0.991, of the gross. Over 30 years that ratio compounds to roughly 0.991 to the 30th, near 0.76. A shortcut that is close enough: the share lost is about the fee times the number of years, less a little, here 30% shading down to about 24%. The shortcut breaks for very long horizons, so give the exact figure when you can.
The relationship
$\text{share lost} = 1 - \left(\frac{1.09}{1.10}\right)^{30} \approx 1 - 0.760 = 24\%$
1.10 gross growth factor, 10% a year
1.09 growth factor after a 1% fee taken off the return
30 years invested
What it says in wordsThe share of final wealth lost is one minus the net path divided by the gross path.
State the convention. Here the fee is taken as one point off the return. If it is charged as 1% of the year-end value, the net factor is 1.10 times 0.99 and the share lost is 26%. Either way the answer is about a quarter, and the limitation is worth saying: the maths treats the 10% as certain, while the fee is paid in bad years too.
Where candidates lose it
The fast wrong answer is 1%, or 10% of the gain. It treats the fee as a one-off slice rather than a rate that compounds. Clients make this mistake all the time, and an adviser who repeats it sounds as though they have never shown a client a fee illustration.
The second loss is giving 24% without saying how the fee is charged. Say the convention in one sentence and note that the other convention lands close by.
What the interviewer asks next
What share does a 2% fee cost over the same 30 years?
Over 10 years instead of 30, what share does the 1% fee take?
How would you show this to a client who says 1% is nothing?
004Inflation runs at 6% a year. What will Rs 1 lakh buy in 12 years' time, measured in today's money?Inflation and real returnWarm upIndian wealth management
Try it first
Your first instinct: what is Rs 1 lakh worth in today's money after 12 years?
Show the worked solution
About Rs 49,700, roughly half. At 6% a year, prices rise to 1.06 to the power 12, about 2.01 times today's level. Rs 1 lakh therefore buys what Rs 1 lakh divided by 2.01 buys today, which is Rs 49,697. The rule of 72 gives the shortcut: 72 divided by 6 is 12 years to halve the value of money.
Why divide by the price rise instead of subtracting the inflation?
Think of the family grocery bill. If a monthly basket costs Rs 10,000 today and prices double, the same basket costs Rs 20,000. A Rs 10,000 note still exists, but it now buys half a basket. Inflation does not take rupees away; it makes each rupee buy less, so today's value is the future amount divided by how much prices have grown. Prices at 6% for 12 years grow by a factor of 2.01, and that factor goes in the denominator.
At 6% inflation, Rs 1 lakh buys Rs 70,496 of today's goods after 6 years and Rs 49,697 after 12 years, so money loses about half its buying power in 12 years, as the rule of 72 predicts.
How do you say this to a client with most of his money in a savings account?
Turn it into a rupee amount he can feel. A fixed deposit that pays less than inflation after tax is losing buying power every year, even though the balance goes up. If his deposit earns 6% before tax and inflation is 6%, his real return after tax is below zero. That is the point of the puzzle: nominal growth is not the same as getting richer. Any real inflation or deposit rate you quote to a client has to be the current published one, confirmed on the day.
The relationship
$PV = \frac{1{,}00{,}000}{(1.06)^{12}} = \frac{1{,}00{,}000}{2.012} \approx 49{,}697$
(1.06)^12 how much prices grow in 12 years at 6% a year
PV the future Rs 1 lakh expressed in today's buying power
What it says in wordsDivide the future rupees by the growth in prices to get their value in today's money.
Check it with the rule of 72: 72 over 6 is 12, the number of years it takes prices to double. Doubled prices mean half the buying power. The exact figure is a shade under half because 1.06 to the 12th is 2.012, a shade over two.
Where candidates lose it
The slip is subtracting: 6% times 12 years is 72%, so Rs 28,000 is left. It treats inflation as a straight line and removes money that is still there. Clients who hear that from an adviser lose trust in every other number that follows.
The other loss is saying Rs 50,000 with no reasoning. Say the rule of 72 first, then the exact figure; it shows you can do it both ways.
What the interviewer asks next
At 4% inflation, how long does it take money to halve?
A client needs Rs 1 lakh a month in today's money at retirement in 24 years. What monthly amount will he need then, at 6%?
Why is a fixed deposit's post-tax real return often negative?
005A client needs Rs 10 lakh in hand from a mutual fund redemption. Forty per cent of every rupee he redeems is capital gain, taxed at an illustrative 12.5%. How much must he redeem?Tax arithmeticCoreMutual fund distributionIndian wealth management
Try it first
Which redemption gives exactly Rs 10 lakh after tax?
Show the worked solution
About Rs 10.53 lakh. Each rupee redeemed is 40 paise of gain, and 12.5% tax on that is 5 paise, so he keeps 95 paise per rupee. Dividing Rs 10 lakh by 0.95 gives Rs 10.5263 lakh. Tax is Rs 52,632 and he is left with exactly Rs 10 lakh. The rate is illustrative; check the current rules and any exemption before advising.
Why does adding the tax on top fall short?
Imagine a shop that adds a 5% delivery charge on the order total. If you want Rs 100 of goods delivered and add Rs 5 for delivery, the shop charges delivery on Rs 105, and you are short. When the tax falls on the amount you withdraw, the withdrawal must be grossed up by dividing, not by adding a percentage. Here every rupee redeemed carries 0.40 times 12.5%, which is 5 paise, of tax.
A redemption of Rs 10.53 lakh is 60% principal and 40% gain; tax at 12.5% of the gain is Rs 52,632, leaving exactly Rs 10 lakh, while redeeming Rs 10.50 lakh leaves Rs 2,500 short.
Why is the gain share of each rupee the same across the redemption?
Because the question fixes it: 40% of every rupee is gain. In practice the gain share depends on which units are sold first, which follows a first-in, first-out order for mutual fund units, and on the cost of acquisitionThe price paid for the units being sold, set against the sale value to find the capital gain. of each lot. The grossing up works for any tax rate and gain share: divide the need by one minus the gain share times the rate. Say that general form after the number.
The relationship
$G = \frac{N}{1 - g\,t} = \frac{10}{1 - 0.40 \times 0.125} = \frac{10}{0.95} \approx 10.53$
N the amount needed in hand, Rs 10 lakh
g the share of each redeemed rupee that is gain, 0.40
t the illustrative tax rate on the gain, 12.5%
G the gross redemption, Rs lakh
What it says in wordsDivide the cash needed by the share of each rupee that survives tax.
Say the boundary plainly. Real capital gains tax has holding-period rules, an annual exemption on some gains, and surcharge and cess on top, and the rates change with budgets. The desk wants the method; the client file needs the current rules confirmed before a single unit is sold.
Where candidates lose it
The trap is adding 5% and saying Rs 10.50 lakh. It feels right because 5 paise per rupee is the tax, but the extra Rs 50,000 is itself taxed, and the client ends up Rs 2,500 short on the day he needs the money.
The second loss is quoting a tax rate as fact. Call it illustrative, give the method, and say the current rate and exemption need to be checked.
What the interviewer asks next
If only 20% of each rupee were gain, how much would he redeem?
What if the first Rs 1 lakh of gain were exempt? How does the calculation change?
Why might you redeem from a different fund to raise the same Rs 10 lakh?
006Two assets each have a volatility of 20% a year, and their returns are uncorrelated. What is the volatility of a portfolio split 50/50 between them?Probability and risk of lossCorePrivate banking
Try it first
Pick the volatility of the 50/50 mix.
Show the worked solution
About 14.1%. Each asset at a 50% weight contributes 10% of volatility. With zero correlation, variances add rather than volatilities, so portfolio variance is 0.1 squared plus 0.1 squared, 0.02, and volatility is its square root, 14.14%. The mix is less risky than either asset alone, with no loss of expected return if both assets expect the same.
Why is the answer not simply 20%?
Walk ten steps east and then ten steps north. You have walked twenty steps, but you are only about fourteen steps from where you started, because the two legs point in different directions. Uncorrelated risks are like steps at right angles: they add by Pythagoras, not in a straight line. Only if the two assets always moved together, correlation of one, would the steps line up and the risks add to the full 20%.
Each asset at half weight carries 10% of risk, and because the two are uncorrelated the risks combine at right angles to 14.1%, against 20% if they moved together and zero if they moved exactly opposite.
How do you write the formula without getting lost?
Work in varianceVolatility squared. Variances of independent returns add, which is why risk calculations square first and take the root last. and take the square root at the end. With zero correlation the cross term vanishes, so portfolio variance is just each weight squared times each variance, summed. That is 0.25 times 0.04, twice, which is 0.02, and the square root of 0.02 is 0.1414. A general rule falls out: n equal, uncorrelated assets of the same volatility give that volatility divided by the square root of n.
The relationship
$\sigma_p = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho\,\sigma_1\sigma_2} = \sqrt{0.01 + 0.01 + 0} \approx 14.1\%$
w each asset's weight, 0.5
sigma each asset's volatility, 20%
rho the correlation between the two, here zero
What it says in wordsSquare the weighted risks, add them, add the correlation term, and take the square root.
Say the limitation, because a private banking interviewer will push on it. Correlations measured in calm markets tend to rise in a crisis, when many assets fall together. The 14.1% is the answer to the question as set; a client portfolio needs a stress view as well as the average one.
Where candidates lose it
The fast wrong answer is 20%, averaging the volatilities. It silently assumes perfect correlation and throws away the whole point of diversification, which is the one idea a wealth desk expects you to own.
The second trap is overshooting to zero. Uncorrelated is not opposite: the risks partly cancel, they do not vanish. Only a correlation of minus one takes the mix to zero.
What the interviewer asks next
What is the volatility of the 50/50 mix if the correlation is 0.5?
With four such uncorrelated assets in equal weights, what is the portfolio volatility?
Why do correlations tend to rise in a market crash, and what does that do to this answer?
007A husband and wife are both 60. Each has a 30% chance of living to 90, independently of the other. What is the chance that at least one of them reaches 90?Retirement and withdrawalCoreWealth management
Try it first
Quick instinct: the chance at least one of them reaches 90?
Show the worked solution
51%. The simplest route is the opposite event. Each has a 70% chance of not reaching 90, so the chance that neither does is 0.7 times 0.7, which is 49%. At least one reaching 90 is everything else: 100% minus 49%, or 51%. For a couple, a plan that ends at 90 fails more often than it holds.
Why not add the two 30% chances?
Think of two friends each with a 30% chance of turning up to dinner. Adding gives 60%, but that double counts the evenings when both arrive. With more people the same adding would soon pass 100%, which is impossible. For an at-least-one question, compute the chance that nobody does it and subtract from one. Neither reaching 90 has chance 0.49, so at least one does with chance 0.51.
With a 30% chance each of reaching 90, the couple's outcomes split into both at 9%, only one at 21% each way and neither at 49%, so at least one of them reaches 90 with a 51% chance.
What does 51% change in a retirement plan?
It changes the horizon. A couple's money has to last for the longer of two lives, not the average life, and the longer of two lives is usually well past either single estimate. If each spouse alone has a 30% chance of reaching 90, a plan that runs out at 90 leaves the surviving spouse short in about half of all outcomes. That is why planners model the joint horizon and a longevity bufferMoney or income set aside to cover the years if the client, or the surviving spouse, lives longer than the planning age. rather than a single life expectancy.
The relationship
$P(\text{at least one}) = 1 - (1-p)^2 = 1 - 0.7^2 = 0.51$
p each spouse's chance of reaching 90, here 0.3
(1-p)^2 the chance neither reaches 90, assuming independence
What it says in wordsThe chance at least one survives is one minus the chance that both do not.
Name the assumption. Spouses are not truly independent: they share a household, a diet and often a doctor, and some studies of couples suggest their lifespans move together. The 30% figure itself would come from a mortality table that has to be checked for the client's circumstances. The puzzle is about the method, not the actuarial figure.
Where candidates lose it
Two answers lose the room: 60%, from adding, and 9%, from multiplying. The first counts the both-survive case twice; the second answers a different question, the chance both survive.
The deeper miss is stopping at 51% without the planning point. The interviewer wants to hear that a couple's horizon is the second death, which pushes the plan longer.
What the interviewer asks next
What is the chance that exactly one of them reaches 90?
If the wife's chance is 40% and the husband's 25%, what is the chance at least one reaches 90?
How would you set the planning age for this couple's retirement income?
008A 3-year bond pays a 7% annual coupon and trades at 95 per 100 of face value. What are its current yield and its yield to maturity?Fixed income numeracyCorePrivate banking
Try it first
Which is higher, and roughly by how much?
Show the worked solution
Current yield is 7.37% and yield to maturity is about 8.97%. Current yield is the coupon over the price, 7 divided by 95. Yield to maturity is the single rate that discounts the coupons of 7, 7 and 107 back to the price of 95. It is higher because the bond also pulls up from 95 to 100 by maturity, a gain current yield leaves out.
What does current yield leave out?
Suppose you buy a gift voucher worth Rs 100 for Rs 95, and it also pays you Rs 7 a year until you redeem it. The Rs 7 a year is the income; the Rs 5 you gain at redemption is extra. Current yield counts only the income, so for a bond bought below par it understates the return, and for a bond bought above par it overstates it. Yield to maturity counts both, and discounts them properly.
The bond's price climbs from 95 to 100 over three years while it pays 7 a year, so its yield to maturity of 8.97% is the current yield of 7.37% plus about 1.61 points from the pull to par.
How do you get close to 8.97% without a spreadsheet?
Use the approximation interviewers expect: yearly income plus the yearly share of the gain, over the average of price and par. Income of 7 plus 5 divided by 3 is 8.67, over an average price of 97.5, gives about 8.9%, within a tenth of the exact 8.97%. Then check the exact rate discounts the flows back to 95: at 8.97%, the three payments are worth 6.42, 5.89 and 82.68 today, which add back to 95 once the rounding is put back.
The relationship
$95 = \frac{7}{1+y} + \frac{7}{(1+y)^2} + \frac{107}{(1+y)^3} \;\Rightarrow\; y \approx 8.97\%$
95 the price paid per 100 of face value
7 the annual coupon
107 the final coupon plus the 100 repaid at maturity
y yield to maturity
What it says in wordsYield to maturity is the one discount rate that makes the bond's future payments worth exactly its price today.
Add the caveat a private banker would. Yield to maturity assumes the bond is held to the end, every coupon is paid, and each coupon is reinvested at the same 8.97%. For a client buying this bond in a portfolio, the credit of the issuer matters as much as the arithmetic.
Where candidates lose it
The common error is quoting the coupon, 7%, as the yield. The second is the current yield, 7.37%, offered as the full return. Both ignore the Rs 5 the client collects at maturity.
The opposite error is adding the whole Rs 5 to one year's income and getting a yield near 12%. The gain is spread over three years, so it adds about 1.6 points, not 5.
What the interviewer asks next
The same bond trades at 105. Which is higher now, current yield or yield to maturity?
If market yields fall to 7%, what does the bond trade at?
What does yield to maturity assume about the coupons, and when does that assumption fail?
009A client regrets missing two stocks on his 20-stock watchlist that doubled last year. Of the other 18, five halved and thirteen ended flat. What would an equal stake in all 20 have returned?Behavioural trapsWarm upWealth management
Try it first
Before you add it up: what did the whole watchlist return?
Show the worked solution
An equal stake in all 20 would have lost 2.5%. Put Rs 1 lakh in each, Rs 20 lakh in total. The two doubles end at Rs 4 lakh, the five halved end at Rs 2.5 lakh and the thirteen flat end at Rs 13 lakh, which is Rs 19.5 lakh. The winners he remembers were two picks out of a list that lost money as a whole.
Why does the regret feel bigger than the numbers?
Think of someone who says they almost bought a winning lottery ticket because the number was one digit off their birthday. Every number was one choice among many; only the winner gets remembered. Hindsight picks the winners after the result is known, which is a choice the client never actually had at the time. This is hindsight biasThe tendency to believe, after an outcome is known, that it was predictable and that you would have acted on it., and it makes the missed gains feel certain.
The client remembers two stocks that doubled, but an equal Rs 1 lakh in each of the 20 on his watchlist would have turned Rs 20 lakh into Rs 19.5 lakh, a loss of 2.5%.
How do you use the number with the client?
Turn the regret into the decision he actually faced. At the start of the year he had twenty names and no way of knowing which two would double. The honest benchmark for a missed opportunity is the whole set of choices available at the time, not the best one in hindsight. On that benchmark his inaction cost nothing: holding cash lost nothing, while the list lost 2.5%.
The relationship
$\bar r = \frac{2(+100\%) + 5(-50\%) + 13(0\%)}{20} = \frac{200 - 250}{20} = -2.5\%$
2, 5, 13 the number of stocks that doubled, halved and stayed flat
20 the whole watchlist, equally weighted
What it says in wordsThe equal-weight return is the simple average of the 20 returns.
Note the arithmetic quirk it hides. A double and a halving look like mirror images, but the double adds Rs 1 lakh while the halving takes away only Rs 50,000. Five halvings still outweigh two doubles here, and the adviser who can show that in rupees wins the conversation.
Where candidates lose it
The trap is anchoring on the two doubles and guessing a positive return. Candidates who do this repeat the client's own bias back to him, which is the opposite of the job.
The second loss is getting minus 2.5% and not saying what it means for the conversation. The interviewer wants the reframing: judge a decision by the choices available at the time.
What the interviewer asks next
If he had bought any two stocks from the list at random, what is the chance he would have picked both winners?
How would you respond if he wants to buy only last year's winners now?
What other bias sits next to hindsight in a client's review of his own record?

010Estimate the gold held by a typical urban middle-class Indian family, first in grams and then in rupees at an assumed price per gram.Estimation and sizingCoreIndian wealth management

Try it first

Which starting point gives the most defensible estimate?

Show the worked solution

About 245 grams, or roughly Rs 24.5 lakh at an assumed Rs 10,000 a gram. Build it by person and occasion: the wife's wedding jewellery about 100 g, older jewellery from the husband's mother about 60 g, festival coins about 50 g, gifts for two children 20 g, and the husband's chain and ring 15 g. Convert to rupees only at the end, at the day's price.

Why estimate grams before rupees?

Ask someone how much their jewellery is worth and they will guess; ask how many bangles and chains they own and they can count. Estimate the physical quantity first, because grams can be pictured and defended, while the price is a separate, changing input you plug in at the end. It also means the estimate survives a change in the gold price: only the last line moves.

A household tally of wedding jewellery, older family jewellery, festival coins, children's gifts and the husband's chain adds to about 245 grams, which at an assumed Rs 10,000 a gram is about Rs 24.5 lakh.

How do you sanity check a number like 245 grams?

Check it against the unit people use. Gold prices in India are quoted per 10 grams, so 245 grams is about 24.5 units. A sanity check that uses a different unit or a different route catches estimates that are off by a factor of ten. Then give a range: a family with a recent wedding might hold 400 grams, a young nuclear family nearer 100. Saying the range shows you know the average hides a wide spread.

Source of gold	Assumption	Grams
Wife's wedding jewellery	sets, bangles, chains	100
Mother's older jewellery	handed down, still at home	60
Festival coins	5 g a year for 10 years	50
Children's gifts	2 children x 10 g	20
Husband's chain and ring	worn daily	15
Household total		245

Every row is an assumption you say out loud; together they give about 245 grams for one urban middle-class household.

Why does a wealth desk ask this? Because gold is the asset most Indian families hold outside any statement the adviser ever sees. A household balance sheet that leaves it out misses a sizeable share of what the family owns, and the Rs 10,000 price here is only an assumption to be replaced with the current rate.

Where candidates lose it

The common loss is jumping straight to a rupee figure, which sounds like a guess because it is one. It also ties the answer to a gold price the candidate is quoting from memory.

The second loss is giving one number with no range. A single estimate for a quantity that varies this much across families invites the question the candidate cannot answer: how sure are you?

What the interviewer asks next

How would the estimate change for a family in a smaller town?
Scale it up: roughly how much gold might the households of one city of 20 lakh families hold?
Why does it matter for advice that most of this gold never appears on a statement?

W_48	portfolio value at age 48, Rs crore
(64-48)/8	the number of doublings between 48 and 64, here 2
r	the yearly return that doubles money in 8 years

R	the absolute return over the whole period, here 150% or 1.5
n	the number of years, here 10
r	the compounded annual rate, often called CAGR

1.10	gross growth factor, 10% a year
1.09	growth factor after a 1% fee taken off the return
30	years invested

(1.06)^12	how much prices grow in 12 years at 6% a year
PV	the future Rs 1 lakh expressed in today's buying power

Try it first

Why count backwards instead of forwards?

What does the share of the last 8 years tell a client?

Where candidates lose it

What the interviewer asks next

Try it first

Why is 15% the wrong annual figure?

How do you get 9.6% without a calculator?

Where candidates lose it

What the interviewer asks next

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Why does a 1% fee cost so much more than 1%?

How do you estimate the share in your head?

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Why divide by the price rise instead of subtracting the inflation?

How do you say this to a client with most of his money in a savings account?

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Why does adding the tax on top fall short?

Why is the gain share of each rupee the same across the redemption?

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Why is the answer not simply 20%?

How do you write the formula without getting lost?

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Why not add the two 30% chances?

What does 51% change in a retirement plan?

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What does current yield leave out?

How do you get close to 8.97% without a spreadsheet?

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Why does the regret feel bigger than the numbers?

How do you use the number with the client?

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Why estimate grams before rupees?

How do you sanity check a number like 245 grams?

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