Retired Indian Army major Dhyan Chand died alone and poor on Dec 3, 1979. He was an Olympic Gold medal winner not once, but three times. Awarded the Padma Bhushan, his statues stand in Vienna, New Delhi, and Medak. His birthday is celebrated in India as **National Sports Day**. Yet Dhyan Chand died alone and poor, away from media glare[1,2,3].

“But that won’t happen to me,” Venky, an IT pro, says confidently, “I am a software professional, earning a good salary, and the IT boom doesn’t appear to be slowing down anytime soon … even if there seems to be a temporary setback just now”.

The second part may be true, Venky, but the same technology revolution that is giving you high salaries will also lead you to Dhyan Chand’s end unless you take the proper steps right now. You may not have realized how the following two factors interact:

1. Salary income stops more or less entirely at retirement, approximately at age 60, but the technology revolution has pushed life expectancies much beyond retirement age.

2. The savings you have been putting aside (At least, I hope you have been saving. Have you been living off your credit card instead?) in bank accounts or fixed deposits will, in the long term, be crushed by inflation.

These are fairly well-known facts, but taken together they will likely lead you to a penniless future. It may be hard to visualize how they interact, so let’s build a numerical picture of your financial life. Although it will still be a simple model, I hope it will drive home the point of this article.

I will first explain some basic principles, then describe the model, and then chart its behavior.

# Real Money

Because of inflation, one cannot directly compare the value of money in different years; instead, one uses real money value that discounts the effect of inflation. For example, if the rate of inflation is 10% per year, 100 Rupees today are equivalent in buying power to 110 Rs next year, or 260 Rs in ten years. A better way to look at this is to say that if you hide 100 Rs in the mattress today, its real value will shrink to 62 Rs in 5 years, 38 Rs in 10 years, 15 Rs in 20 years, and 6 Rs in 30 years!

**Money is like mothballs: it evaporates with time. At 10% inflation, its half life is about 7 years.**

That is, *C _{t}* Rupees

*t*years in the future are equivalent to

*C*Rupees today, given

_{r}*100r*percent inflation per year:

Notice, for positive inflation r (prices going up), Cr is always less than Ct.

# Compounded Annual Growth Rate (CAGR)

The same exponential behavior, but accretive rather than evaporative, can occur for your investments too. This is parameterized by the *Compounded Annual Growth Rate* or CAGR, and your money will grow from *A _{0}* to

*A*in

_{t}*t*years for a CAGR of 100c percent per year according to the next formula. Note that the power term is positive here.

However, after taking inflation into account, your investment in real Rupees grows in *t* years to only *A _{r}*,

Notice that whether the investment grows or shrinks in real terms critically depends on *c* being larger or smaller than *r*.

# The Financial Model

We build a simple financial model of Venky’s salaried life:

Every year, Venky earns a salary, pays 30% income tax, spends 60% of his remaining salary, and saves the rest. One year’s savings plus any earnings during the year from his earlier investments are ploughed back into next year’s investments.

With time and hard work, Venky’s salary grows. His expenses also grow as he starts a family, but he lives within a budget of 60% of post-tax salary. After reaching middle age, his salary plateaus (See Peter’s Principle[4]). After a satisfying career, he reaches retirement age. He retires and then starts living off the earnings coming from his investments, managing his expenses within the same budget that he had in his last year of salaried life.

When his expenses exceed earnings, he has to eat into the capital. Eventually he and his wife run out of money — or this world.

That was a simplified description of the financial model. If you want all the gory details, see the last section, *The Detailed Model*.

# The Trap

So now, using the financial model, we are ready to spell out the salary trap Venky can get into.

Figure 1 is a detailed chart of annual values of salary, expenses, investment earning, yearly investments, and net worth (clbal), when all savings are put in bank fixed deposits (6% CAGR post-tax). Starting salary of 5 (all values are in units of Lakhs: Rs.100,000) grows to 500 in 45 years (don’t laugh – ask your elders how much their salary changed in 45 years). Salary stops at age 60, but expenses continue their upward trend. Amount of investments is labeled net worth: it peaks to 25 crores (One crore is 100 lakhs) at 60, then declines steadily. Venky runs out of money at age 70. Values for every fifth year are given in Table 1.

**Table 1: 60% Spending, 6% CAGR**

year | Salary | Tax | expense | invest earning | reinvested | Net Worth |

26.0 | 5.8 | 1.7 | 2.4 | 0.0 | 1.6 | 1.6 |

30.0 | 10.8 | 3.2 | 4.5 | 0.5 | 3.6 | 12.6 |

35.0 | 23.3 | 7.0 | 9.8 | 2.1 | 8.6 | 44.0 |

40.0 | 50.3 | 15.1 | 21.1 | 5.9 | 19.9 | 117.7 |

45.0 | 108.6 | 32.6 | 45.6 | 14.4 | 44.8 | 284.2 |

50.0 | 234.5 | 70.4 | 98.5 | 33.3 | 99.0 | 653.9 |

55.0 | 344.6 | 103.4 | 144.7 | 70.4 | 166.9 | 1340.0 |

60.0 | 506.3 | 151.9 | 212.6 | 132.1 | 273.9 | 2476.2 |

65.0 | 0.0 | 0.0 | 342.5 | 116.8 | -225.6 | 1721.6 |

70.0 | 0.0 | 0.0 | 551.5 | 16.5 | -535.1 | -260.4 |

75.0 | 0.0 | 0.0 | 888.2 | -203.2 | -1091.5 | -4478.3 |

80.0 | 0.0 | 0.0 | 1430.5 | -634.7 | -2065.3 | -12644.0 |

85.0 | 0.0 | 0.0 | 2303.9 | -1433.7 | -3737.6 | -27632.2 |

The values of 25 Crore net worth, 5 crore annual salary sound unreal. It is better to look at real values that are discounted for inflation. Figure 2 shows the chart for real net worth – a much more believable peak of about 88 Lakhs at retirement. Notice that after 45 years of toil, the nest egg is less than 5 times Venky’s final salary.

Now let us see the effect of investments giving higher yields: 10%, 12%, 14%.

Figure 3 charts real net worth for these CAGR values as well as 6% CAGR for comparison with Figure 2. As the CAGR rate increases, you can afford to live increasingly longer – at 14% CAGR your net worth keeps climbing rather than shrinking after retirement.

**Table 2: Real Net worth for different investment strategies**

year | 0.6 cagr | 0.10 cagr | 0.12 cagr | .14 cagr |

26 | 1.5 | 1.5 | 1.5 | 1.5 |

30 | 7.8 | 8.4 | 8.7 | 9.0 |

35 | 17.0 | 19.6 | 21.1 | 22.7 |

40 | 28.2 | 34.6 | 38.7 | 43.3 |

45 | 42.2 | 54.8 | 63.2 | 73.4 |

50 | 60.4 | 81.9 | 97.1 | 116.7 |

55 | 76.8 | 110.6 | 136.1 | 170.4 |

60 | 88.1 | 136.7 | 176.0 | 231.9 |

65 | 38.0 | 98.9 | 153.4 | 236.6 |

70 | -3.6 | 61.1 | 128.6 | 242.1 |

75 | -38.1 | 23.2 | 101.5 | 248.8 |

80 | -66.9 | -14.6 | 71.9 | 256.7 |

85 | -90.8 | -52.4 | 39.4 | 266.3 |

“Wait, this was with spending 60% of my post-tax salary, that is just 28% of my salary going into savings” Venky says, “I just need to be more frugal, even though I may have a hard time keeping my wife happy”. Well, let us see what the model does with 30% spending and 6% CAGR.

As Figure 4 shows, being more frugal increases peak real net worth so that Venky will run out of money at age 84 rather than age 70. But remember, frugal living may also enhance lifespan. It appears that the problem still remains; Venky has not escaped the trap.

# Summary

Be aware of the salary trap. Even high salaries don’t allow escape from the trap (unless, perhaps, you reach a really high rung of the corporate ladder). Here are the main points:

* Money evaporates like mothballs.

* Income from salary won’t last you much past retirement unless you do one of:

– Live a life of debauchery and die soon after retirement.

– Live very frugally all of your life.

– Invest a reasonable amount of savings such that *on the average* you beat inflation by a good margin.

* Arrange to generate passive income, especially after retirement.

* If your investments cannot beat inflation, it helps to continue working past retirement.

# References

[1] Dhyan Chand. http://www.webindia123.com/personal/sports/dhyan.htm

[2] Dhyand Chand. http://www.indianetzone.com/9/dhyan_chand.htm

[3] Dhyan Chand. http://www.indianexpress.com/oldStory/22333/

[4]. Peter’s Principle. http://en.wikipedia.org/wiki/Peter_Principle

# Appendix: The Detailed Model

The model calculates the effect of savings, if any, being put into investments at the end of each year.

Investments made in the year = Year’s income – year’s taxes – year’s expenses.

Annual income comes from two sources: Salary and returns on prior investments. We ignore your winning the lottery or a large inheritance from an uncle who had run away to Brazil, as being too improbable to count on.

Salary generally increases with age. This is modeled as a linear growth in real money terms, with an additional inflation multiplier.

100s is yearly percent increment in salary in real money

100s’ is the inflationary increment component, typically s’ is less than r, the inflation rate.

An additional complication is that real salary doesn’t keep increasing throughout the employment. It generally stops growing when an individual hits a plateau (see Peter’s Principle[4]). So the factor s would have one value in early years, and a different value in later years. After retirement, of course, St becomes zero.

Thus we have different curves for salary for the three periods defined by the following four points in time:

t0 = starting age = 25

t1 = start of plateau = 50

t2 = retirement. = 60

t3 = death = 85

Salary that comes into your hands is after deduction of income tax. I have used a simple, proportional 100u percent tax rate for each year. T = uS.

Next, we need to model the expenses. I use a simple model for expenditure, and it emulates a conservative, prudent approach to spending: Expenses are modeled as 100*e _{1}* percent of post-tax salary until retirement and then hold the

*real*expense steady in value thereafter. Rate of inflation is

*100r*percent per year.

Next, we come to investments. Although one would make different kinds of investments with different tradeoffs of risk and return, I have clubbed it all into a single average investment, with an average CAGR of 100*c *percent *after taxes*.

Thus the final iterative formula becomes,

Capital at year t+1

C_{t} can also be called net worth. After taking inflation into account, it becomes R_{t}, real net worth.

## Parameter Values

The following parameter values are used to generate the figures used in this article:

Inflation rate = 10%.

salary real increment rate = s = 5%

salary inflation rate s’ = 5%

expense rates, percentage of post-tax salary: e1 = 60%, 30%

income tax rate = 30%

Inflation rate taken at 10% is probably higher than the historical long term average, but I believe that conclusions based on *comparison* of other rates with inflation rate will not be materially affected by the specific value of inflation rate.

## Perl Script

#!/usr/bin/perl -w

# The Salary Trap

############################### Debugging ############################

$PrintDetailed = 1;

############################## Input Parameters ######################

$t0 = 25; # AGE childhood stops

$t1 = 50; # AGE salary growth stops

$t2 = 60; # AGE salary stops.

$t3 = 85; # AGE heart stops.

$TaxRate = 0.30; # tax on salary

$Sal_starting = 5; # in Lakhs per year

$Sal_increment = 0.08; # yearly increase in real money terms t0 .. t1

$Sal_inflation = 0.08; # salary inflation per year t0 .. t2

$Spend = 0.6; # spend this fraction of post-tax salary

$Exp_inflation = 0.10; # yearly inflation in expenses t0 .. t3

$Money_inflation = 0.10; # overall inflation rate

$CAGR = 0.12;

###################### State Variables ###############################

$t = 0; # current year

$inv = 0; # current investments

$sal = 0; # current salary

$exp = 0; # current expenses

$maxsal = 0; # max real salary

$maxyear = 0; # max real salary in this year

######################################################################

# initialize all state variables

sub do_init

{

$inv = 0;

$t = $t0;

$sal = $Sal_starting;

$exp = 0;

$maxsal = 0;

$maxyear = 0;

}

# compute salary

sub do_one_year

{

my ($s, $e, $i, $tax, $savings, $x, $realsal, $realinv);

# $s is salary multiplier, $e is expense multiplier

$t++;

print “year $t opbal $inv “;

if ($t <= $t1) {

$s = (1 + $Sal_increment) * (1 + $Sal_inflation);

} elsif ($t <= $t2) {

$s = (1 + $Sal_inflation);

} else {

$s = 0;

}

$sal *= $s;

print “salary $sal ” if $PrintDetailed > 0;

$tax = $sal * $TaxRate;

print “tax $tax ” if $PrintDetailed > 0;

# consume $Spend of post tax salary upto retirement

# stay at that level with correction for inflation post retirement

if ($t <= $t2) {

# Expenses tied to salary upto retirement

$exp = ($sal – $tax) * $Spend;

} else {

# continue the expense from previous year

$e = (1 + $Exp_inflation);

$exp *= $e;

}

print “expense $exp ” if $PrintDetailed > 0;

$i = $inv * $CAGR;

print “invest earning $i ” if $PrintDetailed > 0;

$savings = $sal – $tax – $exp + $i;

print “invest $savings ” if $PrintDetailed > 0;

$inv += $savings;

print “clbal $inv ” if $PrintDetailed > 0;

# $x <= 1, discounting for real value

$x = ($t > $t0)? ((1.0 + $Money_inflation)**($t0 – $t)) : 1.0;

#print “year $t, discount $x\n”;

$realsal = $x * $sal;

# remember the max salary in real money terms in this life.

if ($maxsal < $realsal) {

$maxsal = $realsal;

$maxyear = $t;

}

$realinv = $x * $inv;

print “real bal $realinv “;

print “\n”;

}

sub do_one_life

{

do_init;

while ($t <= $t3) {

do_one_year;

}

}

sub dump_params

{

print “Tax rate $TaxRate “;

print “Expense $Spend “;

print “Salary incr $Sal_increment “;

print “Salary inflation $Sal_inflation “;

print “expense inflation $Exp_inflation “;

print “Rupee inflation $Money_inflation “;

print “\n”;

}

############### main ###########################

for ($CAGR = 0.06; $CAGR <= 0.14; $CAGR += 0.02)

{

my $x;

do_one_life;

$x = $inv / ((1 + $Money_inflation)**($t – $t0));

print “CAGR $CAGR “;

print “real net worth $x “;

dump_params;

}

print “# max real salary $maxsal year $maxyear\n”;

Filed under: commentary | Tagged: finacial planning, finance, inflation, investment, money, passive income, salary |

Pranav Peshwe, on August 6, 2009 at 3:15 am said:Nice post! The graphics are effective.

I think, working past retirement for few more years is the way to go, in addition to building assets (land, houses, gold) which appreciate and can be liquidated if push comes to shove.

Kalpak, on August 28, 2009 at 6:00 am said:Nice post! Another important point is that interest rates on FDs and savings account will go down as India becomes a developed economy – for example interest rate for a FD in China is about 3.5% hardly enough to beat inflation. Also post-retirement very few people have health insurance and medical expenses eat into the retirement kitty.

few ways out:

– Invest early. Invest in riskier assets early in your career and go on reducing your risky investments as you age. Make compounding work for you instead of against you.

– Never ever ever use retirement savings for buying “dead” assets like a house(in which you plan to stay) or a car.

– Do not take loans as far as possible as the interest rates eat into your saving.

– Become an entrepreneur or work at startups with atleast some stake and earn more than you can in a job.

K J, on September 14, 2009 at 1:15 pm said:I think the following assumptions are not completely true, especially in an Indian setup (or a social setup getting Indianized):

1. That at the old age, which obviously coincides with retirement, lifestyle remains the same as that at the young age.

Who goes to a Eurotrip at age 70? Who goes to buy a new Honda Civic at that age? Who gets married at that age? 😛

In a typical Indian setup, the people tend to become more frugal and abstemious in the old age. Nothing wrong with that, especially if one believes in the four Ashrams of an ideal life (Brahmacharya, Grihastha, Vaanprastha, Sanyaas) as preached by the Vedas. Moreover, an old person’s mind and body also don’t support much lavish and ‘fun’ lifestyles, aiding him/her to slowly cut on the expenses incurred therefore.

Also, when your kids go out when they grow up, say when you’re aged 50, your expenses reduce drastically because now your kids’ education is over and they can support themselves pretty well. Heck, they (can) even send money home. So, you should not assume that your expenses increase (or even remain same) after your kids become self-dependent.

2. That one is totally on his own. It’s just not true in our country. Kids still do support and take care of their ailing old parents. Although the contrary is becoming much more prevalent in our society, but I think the fraction of caring offspring is still good enough.

Suppose a couple has, say 3 kids, and after retirement the expenses of the couple have come down to 50% of their original (as per point #1), which is 50% of the time when they were supporting all the 3 kids and were young themselves. Now, suppose 50% of this new expense is bore by their own savings and returns on investments made. If the remaining 50% is shared by 3 kids equally, wouldn’t that make life so easy for the couple and also their kids?

I know, I made some very simplifying assumptions and also considered quite an idealized scenario, but still I believe there is no reason to panic over money if one has been earning well and saving well and setting up good examples in front of the kids by taking care of one’s own elderly. 😉

Milind, on August 25, 2010 at 5:20 am said:Just browsed through this morning.

Though I thought of this stuff and acted on it, could never worked on a mathematical model for it.

Your is interesting and I will study it over week end and post my findings further.

One thought though, can this model incorporate possibilities of asset growth and windfall returns, etc. to make it more realsitic?

Brigitte, on October 31, 2013 at 9:59 pm said:Having read this I thought it was really enlightening. I appreciate you taking the time and effort to put this article together.

I once again find myself spending a significant amount of time both reading and posting comments.

But so what, it was still worthwhile!