# Innumeracy: Not understanding mathematics!

One professor of a college wrote into a leading personal finance magazine:

“I do not agree with you…Equity is not a great investment.

The Sensex started in 1978 at a base of 100 and in 2007 reached 20,700. This means 207%. Now this means it has given a CAGR (think compounding!) of 6.9%.

We could have got this in a bank fixed deposit, so why invest in equities”

My take: I think he has just confused the issue between ‘TIMES’ and ‘% age’. 207 times in 30 years is NOT 207%. Not sure what he would have done if it was say 20 years or 40 years. Then he has divided 207 by 30 to arrive at 6.9%. Obviously he is wrong.

What is wrong: The way to calculate compound interest or IRR is either to use a scientific calculator or excel sheet – and the answer is about 19.4% CAGR.

What I told him: It was too good an opportunity for me…so I said “Prof., assuming that we got 7% p.a. according to the rule of 72, your money should have doubled in 10 years…so over 30 years what would have happened is 100 to 200, 200 to 400 and 400 to 800. This is the impact of 7% compounding over 30 years. Unfortunately Prof., the sensex is slightly more than 800.

Approximately 20,000 more than the 7% compounding…..

Note: Please do not laugh – when this problem was given to a few qualified people…they could not solve the problem too. So mathematical illiteracy is a serious issue. Not just among students but also of the faculty. So HR people stop cribbing – it is the EARLIER generation that is FAILING us, not the kids themselves ðŸ™‚

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## Manshu

I made a small calculator a couple of years ago to calculate the CAGR if you have the other numbers, as well as the amount if you want to see what a certain CAGR will do for you in a few years.

At the risk of a little bit of shameless promotion….here is the link:

http://www.onemint.com/2008/10/09/cagr-calculator/

Here is another link from MoneyChimp in which the page doesn’t refresh to show the number but you can only calculate CAGR rate:

http://www.moneychimp.com/calculator/discount_rate_calculator.htm

## pravin

not a professor of math,i hope!.its okay for professors in literature,for example,to be ignorant of CAGR .we tend to presume,all academics are good with numbers.our mistake

## subra

sadly professor of finance and life insurance Pravin!

## Dr Mohammed Ali Khan

There is an iPhone application called compoundee..

You can very easily calculate CAGR in it.. Just punch the initial and final amount and the no. of years and the answer is there in a jiffy.. And this 2nd hand iphone I got for Rs 15,000 only.. I have to say, iPhone is an AMAZING phone..

There are 100s of other financial applications.. And they are in your pocket.. So if anybody makes any idiotic comment like this you can make him realize his folly in a minute..

## Asoke

I did a quick survey there is no paper on ‘Investment Mathematics’ even in the CA syllabus, and of course not there in most MBA colleges who specialise in Finance. One paper teaching Arith mean, gm, harmonic mean, data collection and interpretation, std deviation, arr, irr, xirr, compounding, annuity, operations research, assigning probability to events, calculating Expected value, ….my God the list is long! Why there is no paper on this beats me. So to me it is not suprising, but I agree it is illogical..that it is not there!

## bharat shah

i thought yesterday that this is rather extreme case! however today i come across through a marketing literature for its equity share recommendation services based on warren buffet principles, and i found it showing warren buffet assets multiplied his wealth whopping 4344 times over a period of 45 years, but the buffet’s investments it mentioned : washington post-63 times in 37 years, coca cola 16 times in 22 years , gillette 9 times in 22 yrs: surprised me how with such not so great investment warren buffet reached his journey to 4344 times in 45 years ! for proving the warren buffet’s principles when a wellknown financial advising company is giving these examples, whether it is due to their belief of the target clients’ poor knowledge about cagr , compounding etc. or their own (literature preparor’s) lack of knowledge about the same or some genuine mistake in giving the data! whatever may be, i am of the belief , that the real srength of the compounding could be felt only figuring the data.

## subra

bharat ask for the same after fees. I realised when we did a calculation of a few of our friends portfolios on the basis of a 2% amc charge – the results were stunning.

## bharat shah

thank you for your advice between the lines! however double mind whether to go for it is not because for the charge. i am believer of ‘nothing is free’. but my dilema is due to: from last one year so i changed all my family investments from equity shares to equity mutual funds with some information through a well known mf site , after watching my direct equity investment not doing good compared to the index since 2006 after performed good from 2003-06 due to my own limitations. now would it be a good decision to change the track, when the performance of the portfolio is better compred to index, category average. i have great respect for the founder of the said organisation and already its mutual fund is major constituent of my portfolio. i have already subscribed one of their direct equity service , though i have no investment in equity shars at all. all this is as you said in one reply: there are no easy answers in personal finance. any way thank you again!