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How to calculate how many years the capital can be doubled?
Wed, 01/04/2017 - 11:43

Gustavo Neffa

La importancia de la educación financiera en los niños
Gustavo Neffa

Gustavo Neffa es Socio-Director de Research For Traders.

We all want to make money. But long-term obsession often involves the objective that is so simple and difficult to find: doubling capital.

How do I calculate how many years the capital can be doubled? How long it takes to double the capital of my investments is anecdotal, because many times the interest rates are so low that we will not live to see it, but our children or grandchildren will.

To do this, you must understand some concepts of basic financial mathematics, such as compound interest, the geometric mean and a famous rule that has an associated number, which is the rule of the number 72.

Compound interest comes into play when you reinvest your profits (add the gains/losses to your initial capital). Why compound? because each time the revaluation of the previous year is added and the interest is applied again. In this way, interests produce more and more interests, generating a snowball effect.

If you invest about $10,000 at an interest rate of 8% per year, you will reach a capital of $10,800 after one year. But in the second year, if we reinvest the 800 dollars we will not have 800 more dollars at the end of the first year, but more than that, because the capital is added to the 10,800 at the end of the first year, not to the original 10,000. At the end of the second year, you will have 11,664 (and not 800 more; that is: 10,800+800=11,600 dollars. The difference of 64 dollars is the result of having reinvested the profits after the first year.

The reader of this note has just understood in a simple way the benefits of compound interest, that is, the capitalization of profits from previous years. The basic requirement is to reinvest all the profit and contribute the original capital.

How long does it take for an investment to double its money? To calculate how many years the money in a fixed income investment (a bond, for example) could be doubled, you can practice in a simple spreadsheet. Using the numerical example above, one can double the money in exactly 9 years.

A simple calculation is known as the rule of 72, and it is based on dividing the interest rate by 72 to know approximately how many years it takes to double the money from an investment.

If the profitability is 4% per year, it will take almost 18 years to double your capital, but at 10% per year the capital would double in just over 7 years.

The decline in the yield rates on treasury bonds that occurred over the last few decades has led to calculations of an increasingly longer time needed to recover the capital: at 1% annual profitability, it takes about 72 years. to be able to double the capital.

They are not exact calculations but they are valid as an approximation. To make it more perfect, each year consists of 12 months and the decimals must be transformed into months.

In short, it is enough to have that magic number (72) on hand to know how long it will take us to double the invested capital based on the interest rate that an investment gives us:

72= interest rate × years interest rate = 72/years years = 72 / interest rate

Warren Buffett is said to use the rule of 72 to calculate how profitable an investment is.

The requirement of this method is that the interest rate is constant throughout the period. We know that in the real world, the rate of return or the Internal Rate of Return (IRR) is not invariant: it changes from one period to another, so we will not know at what rates we will reinvest our money and what, ultimately, our cost effectiveness. Only if we have a bond at the desired maturity can we approximate the calculation, but not even that way because the coupons must be reinvested and there is no certain future interest rate. The IRR is only an estimate, and it also assumes that all coupons must be reinvested.

*This column was originally published in Sala de Inversión.