Underwater Blues

The New York Times now encourages you to walk away if you have an "underwater mortgage" on a house, that is, you owe more money on the mortgage for the house than its value in the current housing market. I find such analysis based on the negative equity of a house somewhat puzzling. It might make sense if you have bought a house purely for investment, but not if you call it a home that provides you protection against the elements. If you give up your house, you still have to find an alternative accommodation and very likely pay rent for it.

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Stop Taxing the Interest from a Savings Account

It is utterly unfair for the Indian government to impose an income tax on the interest earned by an individual on a savings account. The government merely adds insult to an injury caused by low rates of interest, lower effective yields and high inflation.

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A Dismal Quest

I am looking for a good introductory book on economics to teach myself the basics of this dismal science. From the little I know about it, I have come to realise how important it is in helping one make sense of much that happens in the modern world. I am looking for a book that systematically provides a comprehensive introduction to the principles of macro-economics and micro-economics.

The most popular text for this purpose, till recent times, seems to be "Economics" by Paul Samuelson and William Nordhaus. However, N. Gregory Mankiw's "Principles of Economics" seems to be becoming increasingly popular these days. Fortunately for me, both of these books are available in cheap Indian editions. I flipped through the pages of these books in a bookshop and I must say that Prof. Mankiw's book looks far more approachable to a layman.

I notice that Paul Krugman has also come out with such a book titled "Economics", though I couldn't locate an Indian edition for the book. There are also freely-available economics text-books published on-line like "Introduction to Economic Analysis" by R. Preston McAfee (an "open-source book") and "Principles of Economics" by Timothy Taylor (an advertisement-supported book). I do not like reading lots of text on the computer screen and I cannot order the "dead-tree" versions of these books until I know for sure that they really are better than the more popular alternatives (viz. the books by Prof. Samuelson and Prof. Mankiw).

I would like to ask those of you who are more knowledgeable in economics: what book would you recommend for this purpose?

Calculating Interest Rates

You want to buy that fancy LCD TV that costs Rs 60,000 but you do not have that much money with you. You see an advertisement in a newspaper for the TV from a dealer who offers to sell it to you if you make a down-payment of Rs 10,000 and pay Rs 4,380 every month for one year. You see another advertisement in the newspaper for the same TV from another dealer who offers to sell it to you if you make a down-payment of Rs 20,000 and pay Rs 1,330 every month for three years. How do you calculate the rate of interest each dealer is charging you for what is, in effect, a loan?

In "Calculating EMIs", we derived the formula for calculating the "Equated Monthly Installment" (EMI) on a loan. If "E" represents the EMI, "P" represents the principal amount in the loan, "r" represents the monthly rate of interest (one way of arriving at it is to divide the annual rate of interest, quoted as a percentage, by 1,200) and "n" represents the number of months in the tenure of the loan, then:

     E = P × r × (1 + r)ⁿ / ((1 + r)ⁿ - 1)

In the current example, we know the values for "E", "P" and "n" and wish to calculate "r". Unfortunately it is not that simple to calculate "r" using just the high-school algebra that most of us manage to remember. Fortunately there is a simple algorithm that can help us in this situation.

Let us first rewrite the formula above as an equation:

     P × r × (1 + r)ⁿ / ((1 + r)ⁿ - 1) - E = 0

Our task now is to find the roots of this equation - that is, the values of "r" that will make the left-hand-side (LHS) of this equation evaluate to zero.

To find the roots of a given equation "f(x) = 0", the algorithm in question can be described as follows:

1. Find a value "a" for which "f(a)" evaluates to a negative value.


2. Find a value "b" for which "f(b)" evaluates to a positive value.


3. Let "c" be the average of "a" and "b".


4. If "f(c)" is close enough to zero, "c" is the desired root.


5. Otherwise, if "f(c)" is a negative value, substitute "c" for "a" and repeat the procedure from step #3 and if "f(c)" is a positive value, substitute "c" for "b" and repeat the procedure from step #3.

Note that this is just a binary search algorithm. By "close enough to zero", we mean that the absolute value of "f(c)" is less than some value, usually called "epsilon", that can be as small as we please. The algorithm given above can be rewritten as a function in a pseudo-language as follows:

  guessRoot( f, a, b)
  {
    c := (a + b) / 2;

    if( absoluteValue( f( c)) < EPSILON)
      return c;
    else if( f(c) < 0)
      return guessRoot( f, c, b);
    else
      return guessRoot( f, a, c);
  }

You can implement this in your favourite programming language along with a function that calculates the LHS of the equation given earlier. You can choose a value of "epsilon" according to your preference - the smaller the value of "epsilon", the more accurate is the result and the longer it takes to compute it. The time taken for the computation is also affected by how wide is the range between "a" and "b". Note that Newton's method is a much faster way of computing the roots of such equations, though it involves calculating derivatives.

How do you arrive at the values for "a" and "b"? This differs for each function. For our example, we can start with a low guess of "0.001%" ("0%" gives an undefined result) as the annual rate of interest and a high guess of "100%" and this gives us a negative and a positive value for the LHS respectively. With an "epsilon" of "0.00001", a C programme computes the answer in around 25 iterations.

In our example, the first dealer is offering us an effective loan of Rs 50,000 for 12 months with an EMI of Rs 4,380 and the effective annual rate of interest comes to about 9.32%. The second dealer is offering us an effective loan of Rs 40,000 for 36 months with an EMI of Rs 1,330 and the effective annual rate of interest comes to about 12.08%. In terms of the interest rates being charged by the dealers, you should now be able to tell that the first dealer has a better proposition for you when compared to the second dealer.

Pricing Your Time

We often hear clichés like "Time is Money" or "Lost Time is Lost Money". Most of us generally agree with these assertions but do not actually try to quantify the money associated with our time. We therefore rely on our intuition or mood to decide whether it is worth it to do something ourselves or pay someone else to do it on our behalf.

For example, does it make sense for us to fill out the relevant form and file our income tax returns ourselves or should we just pay the fees to an agent who will do it for us?

Suppose the agent charges 200 rupees for this service, you drive a motorcycle that gives you about 48 kilometres per litre of petrol in city traffic conditions, the price of petrol is 55 rupees per litre, the distance to the income tax office is about 15 kilometres and the parking attendant there charges 2 rupees. If you were to file the returns yourselves (filing income tax returns online is not yet fully available in India), you will directly incur a cost of about 36 rupees in fuel and parking charges. Assuming that it takes about 15 minutes for you to fill the form yourself and about 60 minutes for the trip to the income tax office and back, is it worth saving this time and pay the agent an extra 164 rupees for his service?

A couple of my friends and I used to amuse ourselves by trying to calculate our time's worth using our salary as a guide. Assume that your annual salary is about 4,00,000 rupees, your employer expects you to work about 8 hours every day from Monday to Friday and grants you a leave of 15 days in a year. With about 52 weeks in a year, that is about 246 working days or 1,968 working hours. This means that your employer is willing to pay you about 203 rupees for every working hour.

So in this particular case, at least from your employer's perspective, it is better for you to pay the agent the extra 164 rupees that he is asking for rather than waste about 254 rupees in lost (hopefully productive) time.

Technically we should also consider other factors like the price we are willing to pay to save ourselves the effort (in addition to the time) involved in the task, the amount of trust we place in the agent to do the job correctly and on time, our willingness to share the information about our income with a third party, the amount of masochistic desire we have to do our job ourselves, etc. This is therefore a very crude measure of the monetary value of your time.

A professor of Economics has come up with another formula to calculate the monetary value of your time and you might have your own method of calculating this value. Whatever method you use, these methods can be used to quickly tell if it could be worthwhile to do something ourselves or pay someone else to do it for us.

(I wrote this piece purely for its amusement value - it should not be taken too seriously and should merely be used as an indicator in the spirit of Burgernomics.)

Rolling in Money

"Is Indian IT getting too expensive?" is an article in The Times of India that is a perfect example of the reckless and utterly irresponsible journalism that is increasingly becoming the norm for this newspaper. While the general thrust of the article is more or less correct, either the reporters in question or the "analysts" they consulted seem to have simply made up all these numbers. Believe me, it is not at all the norm to pay a guy with 10 to 15 years of experience an annual salary of 1.5 to 2 crores Rupees (about 330,000 to 440,000 USD)! The numbers are off by about an order of magnitude. I also think a salary of 70,000 USD for a middle-level manager in the US as stated in the article is a bit on the lower side, though I cannot be sure. As a couple of us were joking upon reading this article, these guys should have published the names of the companies which supposedly pay such salaries so that all of us can apply for a job with such suckers. On the other hand, such a company will not last long because it will quickly drain out its cash reserves doling out such largesse.

Unfortunately, these are precisely the kind of stories that unnecessarily widen the divide between software engineers and other sections of the society. They also unnecessarily make software engineers a lucrative target for robbers and other criminals. They create frustration among gullible engineers who think they are never paid enough for their job, even if they are already being paid far more than they deserve. They cause engineers returning to India from the US and elsewhere to demand really outlandish salaries for a job.

Pathetic.