Retirement Equation

When can I retire from my job and live the life I want?

After playing the retirement game, it becomes clear that just having a good job is not quite enough in today’s world. By “good” I mean good pay, of course. And, “job”, unfortunately, often means “practically no family life except on days off”. Hence the popularity of the topic, “how much money does it take to retire from this job?” in company lunch breaks! I noticed this topic started coming up regularly in the IT MNC that I worked in, just after the year 2000 crash. I suppose the realization that one’s job is not secure also became more acute after that year, and seems to have remained quite acute from then onwards.

If you happened to read the analysis of the retirement game, you may have noticed that with certain investing strategies plus some good luck, one can build up a big enough corpus to take early retirement! This observation lead to the present article that will attempt to answer the following question:

How much money do I need to retire from my job right now?

I remember we used to have numerous lunch break discussions around this question, but they never yielded any proposals that everyone could agree upon. The fatalistic camp’s solution was, “You can retire today provided you live within your means”. The pessimistic camp came up with “No amount of money that we can make will allow us to retire”. The engineering camp came up with the simple formula,

Survival period = (Savings) / (expenses)

I think, in those discussions, we all missed the significant role played by the principle of compounding.  Well, this post presents an analysis that takes compounding into account.

What factors need to be taken into account to answer the retirement question? In my mind, at least the following ones:

  • K Rate of inflation
  • R Rate of return on investment
  • T Life expectancy, or time to live
  • X0 Initial Annual expenditure, or lifestyle level
  • P0 Initial net worth (at time of retirement)

These factors can be used to find solutions for these time dependent variables

  • P(t) net worth at time t
  • X(t) Expenditure level at time t

Although the first three factors vary with time and circumstances, and their values can only be guessed (since they relate to the future), we will perform our analysis assuming constant average values, with the expectation that some insights can nevertheless be gained.

Note: This post does not address the question, “how does one accumulate a high net worth?”

Basic Algorithm: We shall start with simple models and then explore the results of a more detailed analysis. In all models, however, the basic idea is the same, and in fact this same algorithm was used in the design of the Retirement Game:

  1. Start with a certain net worth, or principal.
  2. Add return on investments.
  3. Subtract expenses
  4. Repeat from #2 for the next time period

Note, however, both net worth and expenses are moving targets: they vary with time.

Reference values: To get a feel for how the models work, we shall use the following numerical values for our protagonist Sal from the previous post:

  • K Inflation multiplier, pa. 1.075 (that is, 7.5% per annum)
  • R Return on investment, pa. 1.075 to 1.15 (7.5% to 15% per annum)
  • T Time to live from day of retirement. 60 years
  • X0 4.0 Lakh Rs per year (i.e. 33,333 Rs per month)

T = 60 is a reasonable round value for a person in late 20’s or early 30’s. R is post-tax return.

NOTE: 1 Lakh = 100,000 and 1 Crore = 1,00,00,000 = 10 million.

So now let us look at some retirement models:

Return Equals Inflation (R = K) Model

Simplest model to analyze is to nullify the impact of inflation by taking return on investments to equal rate of inflation. Although return will keep pace with inflation, expenses will eat into the principal. Further, in real money terms, expenses stay constant with time. As real principal is steadily consumed to meet real expenses, we get a simple linear relation:

P0 = X0 * T

This, you will recall, is what the engineering camp had come up with. Using our reference numbers, we get:

P0 = 4.0 Lakh Rs/yr * 60 yr = 2.4 Crore Rs = 24 Million Rs

The equation for P(t) is given below. It is obtained by solving eqn 3 described below, for the special case R = K.

eqn01               k = ln(K)           (eqn 1)

Figure 1 shows a plot of P(t) with initial savings of 240 Lakh (blue curve) and 150 Lakh (red curve).


Figure 1: Net worth when return on investment equals inflation

With respect to the blue curve, it is worth noting that a person not sensitized to the dangers of inflation will feel very secure and relaxed for the first 45 years as net worth grows from 2.4 Crore to 15 Crore even after dipping into the principal for expenses. But around the 55th year panic will set in. In the next few years, he is left wondering, “What happened?”. The red curve shows what happens with initial savings of 150 Lakh: the peak is not as prominent, and of course the money doesn’t last as long.

Steady State Model

This model takes a more optimistic view, that return on investments is greater than rate of inflation, to the extent that expenses can just be met without eating into the inflation-adjusted principal. This is a steady state because real principal remains constant, so one can live indefinitely off it.

(R – K) * P0 = X0

P0 = X0 / (R – K)

Thus, if better acumen yields 15% return, i.e. 7.5% above inflation rate, Sal can live a steady state life with a roughly five times smaller P0 (net worth at retirement) than in the previous model:

P0 = 4.0/(0.075) =  53.3 Lakh


We can also turn this equation around. Instead of finding P0 , determine value of return R, for a given P0. Thus for example, given a starting principal of 100 Lakh, Sal will need

R = K + X0/P0 = 1.075 + 4/100 = 1.115, i.e. 11.5% return per annum.

Figure 2 is a plot of required return on investment for varying values of P0. X0 is set to 4 lakh and inflation to 7.5%.


Figure 2: Steady State Model, R versus P0

Some interesting observations can be made from Figure 2:

  1. Sustained returns of 25%, 30% or more are extremely difficult, if not impossible. So small sized initial savings, say 25-50 Lakh, just don’t work.
  2. Beyond a sweet spot of around 100-150 Lakh, critical value of R doesn’t ease off drastically. In other words, it is worth putting in serious effort to increase R even by a few percent, so that you don’t have to keep working longer to accumulate a larger corpus.

Big Bang Model

If return on investment is higher than that required in the steady state model, then real net worth will continue to grow without bound, exponentially. This, of course is the most desirable state! One has to generate a high R and a high P0 to attain this.

A General Solution

Now we address the more general case. Let’s ease into this by first solving for expenses, X(t). Remember, X is annual expenditure, a cash flow rate. X is measured in Rs/year, not Rs.

dX/dt = k X;  X(0) = X0

eqn02          (eqn 2)

Lowercase k in the exponent is related to annual rate of inflation K, as follows. For t = 1 year,

K = X(1) / X0 = ek

Hence k = ln(K). For example, k = 0.07232  (for 7.5% inflation).

Similarly, exponent for return on investment, r = ln(R).

To take a numerical example for eqn 2, the daily expenditure on the first day of the 10th year will be as follows.

X(10) =  X0 e^10k  = 4 * 2.061 = 8.244 Lakh/year.

Divide X(10) by 365 to get 824400 / 365 = 2258 Rs / day.

Now let’s look at P(t). Change in principal P(t) in time dt comes from two factors:

  • Increase due to return on investment in time dt
  • Decrease due to expenses in time dt

That is,

dP = r P dt – X dt

Using value of X from eqn 2, the equation can be written as:

eqn03         (eqn 3)

To take a numerical example for eqn 3, with P = 60 Lakh, X = 4 Lakh and returns of 10% pa (r = 0.0953) on a particular day, dt = 1/365,

Day’s return = r P dt = 60,00,000 * 0.0953 *(1/365) = 1566.74 Rs

Day’s expenses = X dt = 4,00,000 / 365 = 1095.89 Rs

Day’s reinvestment = dP = 1566.74 – 1095.89 = 470.85 Rs

Incidentally, this only looks okay until you realize that due to 7.5% inflation, P lost its value in one day by k P dt = 60,00,000 * 0.07232 *(1/365) = 1188.82 Rs.

Now, solving equation 3, we obtain (for r ≠ k):



Another way to examine equation 4 is to calculate P in real money terms (i.e., discounted for inflation):


Several observations can be made by inspecting equation 4; these are discussed in the next section.

Big Crunch Model

When R is too small to yield Steady State or Big Bang, net worth will eventually drop to zero. If P0 > B, P will keep rising, leading to the big bang model. P0 = B is the steady state model.

Net worth will eventually drop to zero when P0 < B. Let’s explore this case some more.

Case r > k

B  = X0 / (r-k) is positive.

Since P0 < B, P may rise initially due to second term but eventually first term will drag P down. In fact, P will become zero at T = ln(B/(B-P0)) / (r-k)

Figure 3 plots P(t) for several values of P0 and R. Only curves with P0 < B are plotted.


Figure 3: P(t) for several values of P0 (initial savings) and R (return on investment)

Notice how powerful R is compared to P0 :

  • 50 Lakh lasts for 40 years with R=16% but only 22 years with R=14%
  • 50 Lakh with R=16% lasts longer than 75 Lakh with R=12%

Increasing returns has far more impact than increasing initial net worth!

Case r < k

B = X0 / (r-k) is negative. Let B’ = -B.  Then


Here, the first term may cause P to rise but eventually second term drags P down.

P will become zero at T = ln((B’ + P0)/B’) / (k – r)

Figure 4 plots P(t) for several values of P0 and R. Compare with Figure 3. In particular observe that 50 Lakhs initial savings lasts only 10 years at 4% R (fig 4), but 40 years at 16% R (fig 3).


Figure 4: P(t) for R < K

Curtailing Expenditure

An alternative question to ask could be, “given the amount of money I have, how much can I afford to spend?” This post is already quite long, so this question is left as an exercise for the reader (just solve for X0 in eqn 4).

The Retirement Question

So finally, we are ready to answer the question,

“What is the least amount of money needed to retire today?”

The answer comes from eqn 4, which is reproduced below:



T = time to live. Set P(T) to zero and solve for P0:


Figure 5 is a plot of R vs P0 for T = 60, 7.5% inflation, X0 =  4 Lakh pa. Remember that r = ln(R) and k = ln(K).


Figure 5: How much money is needed to retire

So the most truthful answer is:

Well, it depends.

It depends on external factors such as inflation rate and investment climate. It depends on internal factors such as your TTL (time to live), your expenditure levels.

But I think the most important factor is the ability to generate a good return on investment. That, coupled with decent sized initial corpus, should do the trick.

Homework: Experiment with these Excel spreadsheets for your own set of parameters. (Download the zip file. The one with no macros computes #1 and #2. The one with macros also finds #3, but you need to enable macros).

  1. T = how many years money will last, given P0, K, R.
  2. P0 = initial funds needed, given  T, K, R
  3. R = required rate of return, given P0, K, T

Disclaimer: Arguments developed here use a simplistic economic model that certainly differs from reality. In addition, accuracy of the conclusions depends on the accuracy of the input parameters. In other words, beware of GIGO (Garbage In Garbage Out).

Further Reading



[3] How much you need to save to meet your future  retirement targets



Analyzing the Retirement Game

The previous post, “Playing the Retirement Game“, introduced you to a simple financial model for a salaried employee named Sal. If you have not played the Retirement Game yet, you are encouraged to visit and figure out what is the best advice you can give Sal regarding his savings and investments.

To obtain a deeper analysis, I put a wrapper around the game to automatically run it multiple times and generate numbers and charts. Here is my experience with the game.

First observation is that randomness introduced in the game for debt and equity investments causes a large spread in outcomes for a given investment strategy.

Living Purely off Fixed Deposits

When all investments are in fixed deposits, how long does the money last? It depends on the level of savings. Without aggressive saving rates we see a shortfall of 20 to 60 years worth of starting salary. But the good news is that if Sal sets aside a fairly large fraction into savings, he will stay in positive zone.


Score vs expense level, pure FD investment strategy

What I don’t like about fixed deposits is that they lose value with time. So, in one sense, Sal’s scrimping and saving and denying his family the money only goes to support the banker’s lifestyle.

Large Spread in Outcomes with Risky Investments

When the game is run many times with risky investments, most runs will have several loss events, but some lucky runs will have zero or very few loss events. These lucky runs, thanks to the power of compounding, will yield extremely large scores. Conversely, some unlucky runs will yield very low scores. Given below are histograms for pure debt and pure equity strategies.


Pure Debt Investment Strategy, 65% expense rate

Pure debt investment with 65% expense rate (i.e. 35% saving rate) gives a mean score of 1, which is approximately break even. Note that a 35% saving rate with pure debt strategy gives same results as a 50% savings rate with pure FD. To see this in another way, we find that pure debt strategy with 50% saving rate gives a mean score of 30 as against zero for pure FD at same saving rate. Score of 30 means retaining 30 years worth of starting annual salary at the end, a decent sum.

Now let us see what happens with a pure equity strategy. Thanks to the compounding effect, mean score is 3970 at 50% saving, 2624 at 35% saving rate, 380 at 10% saving rate! Thousands of years of annual salary is serious money: Sal can surely take early retirement!

However, there is a downside: although mean scores are high, so is the variability. Here is the histogram for 25% savings rate, which shows that there is a 45% chance that Sal won’t make much with this strategy, but a 35% chance that Sal will do very well, plus  20% chance of doing really really well.

rg3_pureequity_75expratePure Equity strategy with 75% expense rate

Debt to Equity Ratio

How does D/E allocation ratio impact results? We shall approach this question from a different angle: let’s measure only the chances of survival with a given mixed strategy. That is, given a certain allocation strategy, what fraction of trial runs result in a positive score? We will call this fraction the success rate of an allocation strategy.

The figure below charts success rate vs D/E ratio. The curves were generated for varying expense rates. The curves are not smooth because a large enough sample size was not used. This jaggedness is noise and should be ignored.

Debt to Equity ratio is given by a parameter k, D : E :: k : 20-k. Horizontal axis represents k as k varies from 0 to 20. Therefore, leftmost values are for pure equity moving to pure debt at the right.


Success ratio (chance of positive score) vs debt/equity ratio

The figure above is very interesting. We can infer several things:

  • Success ratio is higher for higher saving rates (lower expense ratios). That’s obvious, really: more money Sal puts into savings, more likely will the money last until the end.
  • At lower saving rates, debt tends to reduce survival rate.
  • With higher saving rates, there is a sweet spot. best success rate is at about 60-70% debt. I suspect a mixed strategy tempers equity risk by not wiping out all the capital in less lucky runs (that have many loss years).

Remember, with the way the game is set up, if capital is wiped out post retirement, there is no scope for Sal to earn more money, resulting in an inescapable downward spiral into increasing debt.


I feel this extremely simple model has been successful in delivering several insights — or at least, suggesting some directions on where to explore further, perhaps with more realistic models.

In particular, this game does not allow exploration of a non-constant allocation strategy. Many books and blogs advice starting off with higher risk in earlier years and then shift the portfolio to less risky ones later. A hint of this can be seen in the previous chart — building net worth aggressively in initial years is equivalent to using a higher savings rate in the game.

This is also the right place for a strong disclaimer:

Sal’s world is very simple and in no way matches the complexities of real life. It would be extremely foolhardy to use the numbers presented here to take real life decisions. So don’t do that, and if you still do, don’t blame me!

So for example, Sal can put 50% of his salary in FDs and expect the money to last until age 85. But would you get the same results in real life? Who knows?

Nevertheless, some important lessons can be derived from the Retirement Game (notice these ideas are not at all novel — most financial planning blogs and experts will give similar advice).

  1. Risk free investments do not provide sufficient protection in the long term.
  2. One has to, especially from early on, grow money faster albeit taking on more risk.
  3. Provided you have enough money in play, you can reduce the risk with a mixed portfolio. Although it was not allowed in Sal’s world, one can also use a time-varying strategy: start with high risk high reward strategy but gradually reduce high risk investments in later years.

If nothing more, even if this post encourages you to seriously look at investment options beyond bank fixed deposits, I think this Retirement Game will have served its purpose.

Further Reading

Estimate how much you will need at retirement based on current expenses:

Mathematical models of the stock market –

Playing the Retirement Game

How do I get out of the salary trap?

As should be clear from the previous posts, especially the ones titled Salary Curve, Life Expectancy, and Middle Class Saving Mantras, almost all of us middle class people are squarely in a salary trap. The trap has four walls:

  • Limited (and declining) real income from salary
  • Long remaining  life span after salary income stops
  • Lack of know-how on how to grow one’s net worth
  • Limiting mindset regarding financial matters

The question, of course, is this: is there a way out of the salary trap? Well, there must be at least four ways out of the salary trap — one path for each of the four walls listed above!

Most people will focus on breaking through the first two walls:

  • Increase salary income: job hopping / industry hopping / retraining / second job
  • Continue working beyond normal retirement age

Although these two walls may be pushed back a bit, so to speak, they are very difficult to truly break through.

In this post, we shall focus on the third wall, and examine the effect of increasing one’s know-how regarding savings growth. Please note that this post does not tell you how to increase your know-how. Instead, the focus is on analyzing the impact on one’s life if better saving decisions are taken from the beginning.

To that end, let us look at a simple simulation, what we shall call the Retirement Game. The Retirement Game is an extremely simple financial model of a salaried person named Sal. In the game, you are Sal’s financial advisor and must help Sal get out of the salary trap by advising him on his investment decisions.

An F-minus cartoon

You will basically provide Sal an allocation strategy: what fraction of Sal’s net worth is to be held in each asset class (more details below). At the end of each year, Sal’s portfolio is rebalanced so as to continue adherence to the allocation strategy. This means, for example, if one asset class grows very well, its value as a fraction of total worth will exceed the value decided in the allocation strategy. Then Sal books profits to bring this asset class fraction back to the desired level and buys more of the underrepresented asset class.

Based on your investment suggestions, Sal’s savings will grow or shrink. After retirement, Sal lives off his savings for the rest of his lifespan.

A game needs a way to keep score. The score is the amount of real savings (inflation-adjusted) that Sal has left over at the end of the game. If Sal runs out of money, he will live off borrowed money, then his net worth may become negative at the end. Notice that once Sal gets into debt after retirement, he has no chance to recover, and his net worth will keep spiraling downward.

The objective of the Retirement Game is to understand the impact of taking different investment decisions over Sal’s lifetime.

Now let us get into the details of the game. Remember, we want to keep the game as simple as possible to meet its objective, but no simpler. So most parameters are kept constant, although they will not be constant in real life. Also unlike real life, Sal does not face shocks to his expenses such as sending a child abroad for education, children’s marriages, or expensive illness in family. Nevertheless, with a simpler model, we hope to get improved understanding of the shape of the solution.

Thus, there are just a few knobs and levers to operate in the game.

Constant Parameters

Sal gets a job at age 20, his career plateaus at 40, he retires at 60, and has a natural life span of 85.

Starting post-tax salary is 3,00,000 per year. Salary grows at 15% pa for first 20 years, then grows at 2.5% pa less than inflation rate for the remaining part of his career. Actually, starting salary gets factored out from the final score, so don’t agonize over the starting salary being too low or too high.

Inflation is 7.5% throughout. Cost of borrowing money is 10% pa.

There are only three Investment options with fixed risks and returns (% returns are post-tax). That is, there are no long term boom-bust economic cycles in this game.

  1. Bank Fixed Deposits, 5.5% pa, zero risk
  2. Debt instruments, expected yield 8% pa, risk of 10% loss
  3. Equity, expected yield 15% pa, risk of 30% loss

Yields and risks for Debt and Equity need to be explained. The model is as follows:

An investment may either give a bad return of x2 < 1.0 or a good return of x1 > 1.0 with probability of p and 1-p, respectively, per year. Then

(1 + expected yield) = (1-p) * x1 + p * x2


x1 = [(1 + expected yield) – p * x2 ]/(1-p)

Now,  expected yield and x2 are known. As value of p is varied (higher p represents more volatility), x1 will be change correspondingly to keep expected yield at the set level. For example,

1.15  = 0.90 * x1 + 0.10 * 0.70,  then x1 = 1.20 (i.e 20% profit)

1.15 = 0.80 * x1 + 0.20 * 0.70,  then x1 = 1.2625 (i.e. 26.25% profit)

By keeping p as the independent variable, we can better study the effect of market volatility on playing the retirement game.

We also need to model expenses incurred by Sal every year. The model we will use is not too complicated, but should reflect some of the ups and downs in expenditure that happen in real life.

We start with fixing a base level of expenditure at the start of the game, when Sal starts out a bachelor, but over the next 20 years his expenditure grows at the same rate as his salary does, that is, at 15%. However, after age 40 Sal switches to a constant lifestyle, so until retirement his expenses just keep pace with the inflation rate. At retirement, Sal cuts down his lifestyle by 50%. However, with time, expenses again rise with inflation. Since level of savings is an important decision, base level of expenditure is a tunable parameter. Yes, I agree, this is an extremely simplistic model!

Knobs and Levers

You can set the following knobs at the beginning of the game:

  1. Base level of expenditure, as a percentage of starting salary.
  2. Investment allocation decisions. What percent is put in Fixed Deposits, Debt and Equity. In this simple game, allocation strategy is constant throughout.
  3. Number of runs. Since debt and equity investments have randomized returns, play the game many times to get a better understanding.

There is only one lever: hit the [start] button to start the runs!

Note: Although one could chose a design where the expenditure and investment decisions can be changed every year, I have chosen to keep them constant for two reasons. First, it keeps the game simple so it’s easier to measure the effectiveness of a particular strategy that is applied consistently. Second, because random elements are involved, a proper analysis will require the same game to be run many times, which is easy to do when all the knobs are set only once at the start of the game.

Running the Game

We run the game in one year time steps.

At the end of each time step, do the following:

  • Compute changes for one time step
    • Case positive net worth: Calculate returns on existing investments
    • Case negative net worth: calculate interest on borrowings
    • Add gains or losses into current net worth
  • Compute current savings = salary – expenses
  • Compute new net worth = current net worth + current savings.

Note that current savings and net worth can each be negative. Returns on investments may also be negative.

End the game at age 85.

At end of the game, compute score as the following dimensionless number.

score = real net worth / starting salary  , or, in other words,

score = net worth adjusted for inflation / starting salary

Note: Since this game always ends at age 85, we did not really need to discount net worth. But if we ever make the lifespan variable, inflation-adjusted net worth will be required. Also, inflation-adjusted values are easier to understand.

One can interpret a score of N as ending at age 85 with a net worth equal to N years of annual starting salary.

Play the Game

The Retirement Game is hosted at visit this site where you will find the link for playing the retirement game.

If you want to study the code and perhaps modify it, it is also available for download:  download and unzip to get a folder named RetirementGame. Its major functionality is in the associated JavaScript file.

In a few days, I shall publish the next piece, which analyzes the Retirement Game using more powerful tools.


Many thanks to:

Manas Sathe provided invaluable help with detailed review and a critique of the model.

Sandeep Ranade pointed me to Github Pages where the Retirement Game could be hosted (WordPress effectively does not allow JavaScript).



Real Estate : India’s Housing Bauble

Most Indians I have met either already own a house, or very much want to own a house. Their dream house may have one room or ten, but there seems to be a pervasive cultural belief that life is incomplete, even unsuccessful, without having a house of one’s own. This belief shows up in many ways — in lunch hour conversations, discussions at home comparing relatives, in the marriage market, in movies, in sayings such as “roti kapda aur makan” (“bread, cloth, and house”). Hence the “bauble” in the title — the ultimate shiny object!

Now I am not sure where this cultural imperative comes from, nor if this is peculiar to India. Is owning a house an essential status symbol for the Indian middle class family? Or does living in a rented house somehow stunt the soul? I don’t know. Perhaps searching for answers to such questions could be a nice line of research for psychologists or anthropologists.

However, what we could do in this article is to look at the purely financial issues with respect to buying a house versus renting a house. To be more precise, buying a house on mortgage vs renting a house. My strategy for doing a fair comparison is as follows: consider all the cash flows involved in buying a house against a loan, all the way to when the loan gets paid off, and then calculate the internal rate of return based on the salable value of the house at that future time. Next, we consider the alternative, that is, take on rent the house that was bought in the last scenario, and track cash flows over the same period of time. To keep the comparison fair, we invest any surplus cash flows available in the rental case. That is, if the rental scenario requires N Rupees less outflow per month, we put N Rs per month in investment. These two simulations are run until the mortgage ends, then compare the internal rates of return for the two scenarios.

It should be immediately obvious that there cannot be single answer to the “buy vs rent” question; it all depends upon the values of the numerous parameters involved. The decision is fuzzier because many of the parameters are related to the future and cannot be known today. But I believe it will be useful to run this model through some set of numbers and get a better feel for the shape of the problem. If you have a different set of values for these parameters for your specific situation, you can use this spreadsheet to generate your own analysis.

Let us begin by listing the input parameters:

Buying a house

  • Present cost
  • Margin money (down payment)
  • Stamp duty and levies
  • Interior & Furnishing cost
  • Mortgage term (n years)
  • EMI value (cash outflow per month)
  • Income Tax benefit on loan interest
  • Property appreciation % pa
  • Yearly expenses (i.e. property taxes, society charges)
  • Inflation in yearly expenses % pa

Renting a house

  • Deposit amount
  • Rent amount (cash outflow per month)
  • Income Tax benefits on house rent
  • Rental inflation rate % pa

Investing the surplus

  • Returns % pa


  1. We ignore costs of running the house, such as electricity payments, that are assumed to be the same in both scenarios.
  2. For a fair comparison, the two scenarios should use equivalent, preferably identical, houses.
  3. To keep the calculations simple, it is assumed that the various % rates stay stable over the whole duration. Alternatively, take these to be the average % rates over the tenure of the simulation.
  4. Although mentioned above for the sake of completeness, I have left out the impact of income tax benefits from this analysis for several reasons: tax calculation is complex; benefits are capped at fairly low levels; cannot predict how the caps will change in the future. Both sides get benefited, so I feel the inaccuracy from ignoring this factor will be small.

Now, setting out to get good estimates of all these input parameters from the internet was not as easy as I expected. Here is a brief description of how the data was collected.

Property appreciation

Historical property rates are difficult to find. I had to combine property rate indexes from several sources that span different periods into a single chart shown in Figure 1, and that too has a span of only 13 years. The government has now started publishing a residential property index (RESIDEX) for major cities, so we should get good data going forward. The average annual appreciation for Mumbai works out to 15.4%. This is based on data. Corresponding graphs for other cities are quite different, see Figure 2, also based on data, that starts at 2007. Figure 2 indicates that Bengaluru and Hyderabad are in doldrums: zero if not negative appreciation with respect to 2007. Mumbai, Delhi, Ahmedabad, Kolkata are around 15% since 2007, while Chennai property appreciated at a strong 30%, at least up to 2014.


Figure 1. RESIDEX for Mumbai, 2001-2014


Figure 2: RESIDEX chart for several cities, 2007-2014

Rental Rates and Rent Appreciation

Historical rental data is even harder to find. The one consistent message from several sites is this: these days, annual rental yields relative to property price weigh in between 2.5 to 3.5%, although historically the yields have been said to be as high as 7-8%.  A real estate agent in Pune tells me that rent appreciation is closer to 5% per year overall, notwithstanding the typical 8 or 10% rent escalation clause found in multi-year leave and license agreements.

Inflation Rate

CPI inflation has been computed for past 50 years and this is readily available, see my previous post. We take an average inflation rate of about 7.5%.

Margin Money, EMI Calculation and Mortgage Term

Major loan houses seem to ask for 15-25% margin money. I have taken 20% as representative. So for a 125 Lakh house the margin money is 25 Lakh and Loan amount is 100 Lakh.

Most sites are wary about disclosing EMI calculations to anonymous visitors, but several housing loan aggregators peg the current house loan rate for major loan houses to 9.5-10.5%. Luckily for us, ICICI has a nifty EMI calculator where you can input loan amount, interest percentage, and tenure of loan. I have used this to generate some EMI values:

Loan Amount 100 lakh, Interest rate 10%, Tenure 15 / 20 years: EMI 1,07,460 / 95,500 Rs. Alternatively, one can use the PMT function in a spreadsheet:

PMT(rate, intervals, principal) → EMI

Investment Rate of Return

Different sites give different figures, some claiming as high as 35% pa. But I would estimate long term post-tax SIP returns on debt and equity to be around 10% and 15% respectively (see mutualfundinda and jagoinvestor). So we will go with a conservative mixed 40/60 portfolio figure of 13%. I will also run the calculation with a more aggressive equity allocation, considering a young couple could take on more risk.

Yearly Expenses on House

Major recurring expenses on the self-owned house are property taxes and society maintenance charges. Again, these vary widely, good data is not available, but a rough estimate for property tax would be around 0.5% pa of property value (e.g. pcmc doc here). Property tax amounts for a given house increase somewhat with age, but erratically. In absence of any data at all, let us just take a wild guess, say half the CPI for property tax appreciation (3.7% pa).

Society maintenance charges vary a lot based on society expenditure levels and amenities offered. We make a guess again, say 0.75% of initial property value. I think it is safe to assume that maintenance charges will follow inflation (7.5% pa).

Stamp Duty and Levies

There is stamp duty calculator for India. That gave the following values for a 125 Lakh Rs house in Maharashtra:

Stamp Duty : 6,25,000 Rs

Registration Fees: 30,000 Rs

Local Body Tax: 1,25,000 Rs

Total: 7,85,000 Rs (i.e. ~6.3%)

Interior and Furnishings

Sky’s the limit for interiors! But considering that the house is being bought on loan, probably a more prudent budget can be assumed. So a sort of “livable, nothing extravagant, but long lasting” kind of interior would likely take around 10-20% of the property value. We take 15% as a nice round number for our calculations. This is based on feedback from two practicing interior designers-cum-architects, by the way.

Now that we have arrived at a certain set of starting parameters, some from good data, but many from educated guesses, it is time to do the analysis!


Figure 3: IRR variation with change in upside of buy (property appreciation) or rent (investment returns)

The analysis is available here for you to experiment with (but see the disclaimer at the end). The results can summarized as follows:

  1. For BUY, if the upside (property appreciation rate) is higher than the downside (mortgage interest rate), net IRR is positive.
  2. For RENT, if the upside (investment returns) is higher than the downside (rental yields),net IRR is positive.
  3. For same % values of upside, BUY is ahead of RENT by 0-3% (see Figure 3).
  4. Alternatively, if you can make more with investments than from property appreciation by a few percent, RENT wins.

Although these results were contrary to what I expected before beginning this analysis, a little further thought makes it clear why BUY has a small advantage over RENT:

Provided property growth rate is higher than mortgage interest rate, delaying repayments is to your advantage, because your property begins to appreciate from day one while you repay over next 15 years. In the case of rent, investment effectively as an  SIP (Systematic Investment Plan) does not have this advantage. In addition, since the actual rent outflow is higher than expenses on self owned house, this reduces amounts available for investing, dragging down the returns somewhat further.

One issue that is not brought out by the numbers is the question of risk. In the BUY case, you are taking on a single big risk. It is difficult to predict the future. If your income stops due to economic disruptions, or due to health issues or disability, the house itself may be lost.

Therefore, it is prudent to not commit all your disposable income for mortgage payments. So perhaps the best strategy may be, in a sense, a mixed one – that is, buy a smaller house with affordable EMIs and grow the remaining disposable income with proper investments.

Disclaimer: This Buy vs Rent analysis is based on lots of guesswork, forward-looking estimates, and data picked off the internet — use for real-life decisions at your own risk!

Acknowledgments: Thanks to M/s Vrushali Kale and M/s Anita Bhinge for inputs regarding interior costing. A big thanks to Manas Sathe for reviewing the post and helping polish the spreadsheet.

Further Reading ,

Middle Class Savings Mantras: Have They Stopped Working?

Are the savings mantras of the middle class — savings strategies of the middle class — that were the favorite of our parents and grandparents, still sound and useful these days? The general strategy was to put money in the following avenues as a means for long term investment:

  • Fixed Deposits (also called Bank Certificate of Deposit)
  • Life Insurance (as investment, not for insurance)
  • Gold (as investment, not as jewellery)

Do these make very good sense these days? Let’s do some analysis.

Fixed Deposit Mantra

In order to compare the power of fixed deposits over a time span greater than a couple of years, one has to take at least these three factors into account:

  • Rate of interest of FD
  • Income Tax rate
  • Inflation rate

The analysis proceeds like this, for each year:

  1. Take average 3-5 year FD interest rate
  2. Subtract income tax rate from above – this gives ‘post-tax FD’
  3. And then subtract inflation rate (CPI) – this gives Effective FD rate ‘EFD’

Thus, EFD is inflation-adjusted post-tax FD interest rate.

There are several assumptions and estimates involved in this process, so do not accept the final numbers as gospel truth. Nevertheless it is interesting to see how FD’s, based on this analysis, have performed over the years.

Values for FD rate, post-tax FD, CPI and EFD are plotted in figure 1 below.


Figure 1: Effective FD Interest Rate

From the data, several interesting trends over the past 25 years can be noted .

  • Income Tax rates have dropped more or less steadily from 55% to 33%
  • FD rate roughly tracks the inflation rate (except for CPI glitches in 1998 and 2009)
  • EFD is negative in 20 years out of 25
  • average EFD is -2%

It is easier to study effective FD rate in Figure 2 below, where only EFD is plotted.


Figure 2: Effective FD rate (alone)


So it appears that for those at the top income tax bracket , fixed deposits have negative returns, -2% on average. Is the situation better for a person at zero income tax bracket? Turns out, not by much: FD-CPI is just +1.5% on average.

Personally, I began this analysis expecting to find that FDs had decent returns in previous generations but had became ineffective only in the recent past. But it appears that effective yields from FDs haven’t changed much in 25 years.

Possibly these three factors — CPI, tax rates and FD rates — are interconnected so as to keep the EFD at more or less zero.

Sources for FD rates:



[3 ]






Life Insurance Mantra

-How Opal Mehta Got Life Insurance, Got Wild, and Still Got Screwed

Before we begin, please understand: I am not against the concept of insurance, be it car, house, accident, or life. It is a good idea to mitigate the effect of low probability but high impact black swan events by offering frequent prayers at the altar of an insurance company. But what ‘joss sticks’ or agarbattis ought we to burn at this altar? Only those made from term insurance premiums.

“Term insurance” is “pure” insurance: only the risk is covered. So you get back nothing if the dreaded event did not happen. In general, term insurance premiums are lower.

However, insurance agents get paid commissions that are a percentage of the premium amount paid by the client, and to maximize their income, they would rather peddle high premium policies. I have not met a single insurance agent who is even willing to talk about term insurance. They would rather that the clients do not even know that something like term insurance exists. So what do the agents want to offer? Policies that could be called cover plus investment. That is, pay a term premium plus an investment amount. You get a return on the investment amounts which presumably the insurance company will invest and return back many fold. And this investment is even tax free! That sounds great, but after deducting as much as 25% agent commissions plus operational costs plus insurance cover cost from each premium, the people at the insurance company have to be very very savvy to generate a good return for the client from what is left over.

So here is a true story (some details are changed but the numbers are accurate and will illustrate my point).

One day in 2004 Opal Mehta was still feeling annoyed by an income tax audit and when a life insurance agent promised 7% tax free annual rate of return on premiums, plus possibility of additional bonuses, she trusted him. Especially because FD rates were low, around 6% in 2004.

So from 2004 to 2011, for 8 years, she paid yearly life insurance premiums of Rs. 20,560 and in the ninth year, 2012 she got back a total of Rs. 1,91,100. That amounts to 16% net return in the ninth year. Now, the correct method to estimate the annual returns on regular multiple payouts is to compute internal rate of return or IRR. In this case:

IRR  = 3.32%

Note that the FD interest rates post-tax averaged 5.25% during 2004-2011. Now which would have been a better investment for Opal, even given only these two options?

Gold Mantra

Indians have an emotional and cultural attachment to gold; gold ornaments are an essential part of the Indian psyche. But how has gold done in the long run as an investment avenue? Figure 3 charts the average gold price in India for the last 50 years[1].


Figure 3: Historical Gold Prices since 1964


From the above figure, it is clear that up to 2012, gold prices have shown a more or less steady rise, except for a sideways move during 1997-2002. Compare above prices with gold prices in USA (note: both time duration and price units are different), shown in next Figure 4:


Figure 4: Gold prices in USA, $/g

Note that before 1970, US gold price was pegged to the dollar, so the steady rise in Indian gold prices before 1970 despite the US market being mostly flat, can be explained by the erosion in the dollar-rupee exchange rate.

Gold prices in India have not fallen as steeply as in USA since the high of 2013. This may be due to import restrictions but this difference may not last long.

So what does it all mean in terms of gold as an investment opportunity? Take a look at Figure 5 that charts the average annual price rise over a rolling ten-year period.  As an example, the peak of 25% in 1981 means that had you bought gold in 1971 and sold it in 1981, you would have made an annual profit of 25% (Almost a ten-fold return in ten years). On the other hand, buying gold in 1992 and selling in 2002 would have given very poor returns.

Figure 5: Ten year Rolling Average Gains

So it appears that the gold mantra did hold up well until the eighties, and then again after a lull of a decade, it showed a very unusual upward run during 2000-2012. However, market is going sideways again for the past few years, so today It is difficult to claim that it is a good time to buy gold as an investment. Or that it is a bad time to buy gold.

Sources for gold:





Life Expectancy

One of the important issues discussed in a previous post, Salary Curve, is how to make savings last beyond retirement. This is obviously tied to how much the income earner (and spouse) is expected to live post retirement. If the subjects leave this world five years after retirement, most likely their savings will last till the end.

But for Indians, the equation has changed dramatically within the last few generations.

Let us look at some world bank data for India [1] for life expectancy at birth.


The trend is quite consistent.  Life expectancy is seen to increase by one year every two years – that is, by 10 years every generation (20 years [2]). Life expectancy in many European nations was about 80-82 years in 2014, compared to 68 years for India. This leads me to expect that the upward trend in the graph is likely to continue for another decade, although the rate of increase has already tapered off to one year every 2.5 years.

One can draw some disturbing conclusions from this data:

  • A person can expect a life expectancy to be higher by about 10-20 years compared to his parents and grandparents.  Financial planning will therefore be different than what was needed by parents and grandparents
  • Increasing life expectancy means a larger burden being placed on future generations – having to take care of grandparents as well as parents. And who knows, maybe great-grandparents too.

[1] Life Expectancy data

[2] Generation gap


We mentioned, in “Salary Curve”, that total lifetime savings equaling sum of (income – expenditure) as shown in the last curve does not work out in practice because of inflation. Let’s dig deeper into the meaning of inflation, how inflation may be measured, and what it means to you and me in daily life.

Defining Inflation

The qualitative meaning of inflation is simple enough: a sustained rise in general price levels in goods and services in an economy over a period of time [1]. So for example, Rupee prices of bread, soap, and toothpaste in the corner grocery shop near my house are higher today than they were a few years ago.  So it is clear that prices inflate (or currency deflates). A very narrow “point” definition of inflation can be given without much disagreement as follows:

For a specific commodity at a specific location, if its prices at two times T1 and T2  are P1 and P2 respectively (where T1 > T2),


The above gives a multiplier. An alternative formula measures the percentage rate of change:


Computing Inflation

Giving a single quantitative definition that everyone would find useful, however, is not easy. The problem is that ‘point’ inflation varies across commodities, across locations, and across times. It is rather like the concept of density in a non-uniform material.

So one has to develop a method to somehow average these countless point inflation values into a single meaningful value. There are several choices to be made:

  1. How to ‘mix’ the price of two commodities, say soap and SUV.
  2. How to select a manageable number of commodities from the millions of goods and services out there. Do we include soap? Which brands? Which sizes? Which packages?
  3. How to select the locality or area over which prices are to be collected. Town, District, State, Country, …? Or by socio-economic group?
  4. How to select the time interval.

Long story short, the accepted methodology is to calculate a number, called a consumer price index (CPI) at a given time and in a given area as follows:


The Pi values are average prices for specific commodities over the desired area, and wi values are weighting factors that fine tune the contribution coming from each commodity.

This set of commodities is called a basket of commodities.

The rationale for introducing weighting factors comes from quantifying how much money a typical family with typical needs would spend in a month. This can be explained with a simplified example: Consider a family who consumes, on average, the following quantities in a month:

  • soap : 2
  • Toothpaste: ½
  • Bread: 24 loaves


Then a price index based on a basket of {soap, toothpaste, bread} will have the weighting factors {2, ½, 24} respectively. Note the prices and weighting factors must be in consistent units.

Although a single CPI value is not very useful by itself, but CPI values c1, c2 for two times T1, T2, (T1 < T2) can be used to measure inflation in terms of the rate of rise of CPI with time.


If the time interval is 1 year, this gives a yearly inflation rate. If the time interval is 1 month, the yearly rate is derived by appropriate adjustment.

An example of a real-life CPI basket that is specified by Govt of India is described in [3], see Annexure V, pages 137- 144, in particular.

Fuzziness in Inflation Numbers

CPI numbers as published by Govt of India or World Bank have many assumptions and approximations. For example, the basket used for CPI is not that meaningful for the very rich or the very poor. Averaging over a large area or population smears out local idiosyncrasies. The composition of the basket has to be adjusted from time to time to accommodate changing trends.

What it Means to You and Me

CPI-based inflation numbers show a trend. What is really important is not whether inflation is really 6.21 % or 6.53 %, but that in the long term, inflation becomes a force that is very dangerous to your and my financial well-being. But this line of thought will be followed up in a separate article.

Everything is Too Expensive

The other side effect of sustained inflation is that we generally get stressed out because our sense of prices of things lags behind reality. Our expectation of the price of a loaf of bread is probably its price we stored in memory some years ago (most people buy a bunch of things at a time and never pay attention to individual prices). Our expectations often become “anchored” to an earlier year. I suspect that older people are anchored to earlier times than younger people.

Another way to think about this is, everything is not getting expensive really, it is just that the currency is losing its value, year on year.

Unfortunately, when it comes to salaries, this anchoring effect may lull us into a false sense of comfort: what one is getting paid today, even if it feels like a comfortable salary, is probably not much higher than our expectations that are still anchored to salary levels of a few years back. In fact, current salary may be less than earlier years’ salary after taking inflation into account.

Finding Your Anchor Year

So let’s try an experiment. Find a common commodity where you are not aware of its current price. Write down what you feel would be its price today, F. Then find out the actual current price P.

The ratio P/F gives you a multiplier, which is a measure of mismatch between your view of prices and the reality. If you are in India, use the table below to find the closest matching cumulative inflation multiplier and read off the year in the previous column (If outside India, you can construct your own table from [4]). The table below was built from data in [5].

Notice that the multiplier values increase as you go back in past. Consider that the multiplier is 2.01 for 2008. For example, if you feel that a thing that you expect to be priced Rs 50 is actually Rs 100 today, then P = 100, F = 50,  P/F = 2.0, hence you are mentally still in 2008 for this particular item!

This procedure gives you your anchoring year for a particular commodity. Repeat for several different commodities and see if you get a consistent value for the anchoring year. You can now use the multiplier of your average anchoring year to revise all your price estimates upward.That should somewhat reduce the stress from the feeling of paying too much every time you shop.

This anchoring effect works in reverse on income too. So you should  divide your current salary number by the same multiplier, so that you develop a more realistically prudent approach to spending.


2016 1.00 2006 2.26 1996 3.92 1986 9.71
2015 1.06 2005 2.38 1995 4.30 1985 10.40
2014 1.13 2004 2.47 1994 4.70 1984 10.94
2013 1.23 2003 2.56 1993 5.11 1983 12.31
2012 1.37 2002 2.65 1992 5.52 1982 13.30
2011 1.45 2001 2.78 1991 6.24 1981 14.99
2010 1.59 2000 2.88 1990 7.09 1980 16.35
2009 1.83 1999 2.89 1989 7.48 1979 18.27
2008 2.008 1998 3.34 1988 8.13 1978 18.54
2007 2.118 1997 3.55 1987 8.89 1977 20.00

 Table : cumulative inflation multiplier with 2016 as reference (India)


Inflation is the slow but inexorable rise of prices, or conversely, the inexorable loss of value of a currency.

Inflation may lead to shopping stress – “everything is so expensive” – because we often are mentally anchored to price points of an earlier time. Because of this anchoring, it may also lull us into a false sense of security when it comes to current and future incomes.

So inflation may be a mere annoyance in the short term, but over a longer time span. if inflation is not taken into account, it can seriously upset our financial calculations.


[1]  Inflation

[2]  Consumer Price Index

[3]  CPI Manual India 2010

[4]  World Bank Inflation data

[5]  India CPI 1958-2015