Private Wealth Management puzzles, solved step by step

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All topicsCompounding and doubling8Returns arithmetic9Fee and cost drag8Inflation and real return7Tax arithmetic7Probability and risk of loss9Retirement and withdrawal8Fixed income numeracy8Behavioural traps8Estimation and sizing8Options and structured products6Leverage and borrowing6Wealth business economics8
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  1. 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.

    What Rs 1 lakh buys, in today's money, at 6% inflationRs 1,00,000Todayprices x 1.00Rs 70,496After 6 yearsprices x 1.42Rs 49,697After 12 yearsprices x 2.01About half:72 / 6 = 12 years
    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=1,00,000(1.06)12=1,00,0002.012≈49,697PV = \frac{1{,}00{,}000}{(1.06)^{12}} = \frac{1{,}00{,}000}{2.012} \approx 49{,}697
    (1.06)^12how much prices grow in 12 years at 6% a year
    PVthe 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?