# Exploring compound returns - DFSIN - SFL

The Investopedia website recently provided a bit of fun for its readers by asking them to choose one of two options. Option 1: they would receive one million dollars in cash today. Option 2: they would receive… one cent. But tomorrow, they’d receive two cents, and every day after that, for 30 days, they’d receive double the amount of the previous day.

Which of the two options would be a better choice?

As shown in the following graph, the second option is more profitable – by an impressive margin: on Day 30, the person would receive no less than \$10.7 million.

## Rediscover compound returns

The phenomenon behind this demonstration is a concept we are all familiar with, without always understanding its full potential: compound returns. Obviously, the example is not very realistic, since it assumes that the person’s capital is doubling every day, for a daily return of 100%.

However, what many people call the “magic” of compounding could produce impressive results, even at more realistic rates of return. To understand it, we have to compare the concept of a “compound” return with that of a “simple” return. Suppose you invest \$100,000 at a rate of return of 5%*. After one year, you would collect \$5,000. If you withdrew this money and left your initial capital invested, the same rate of return would get you another \$5,000 at the end of the second year, for a total of \$110,000. Your capital would increase arithmetically: this is known as a simple return.

However, if, at the end of the first year, you didn’t withdraw the \$5,000 you made, but left it invested, during the second year your 5% rate of return would be calculated on (\$100,000 + \$5,000) and would thus generate not \$5,000, but \$5,250. In the third year, your return would be \$5,512.50, and so on. Your capital would increase exponentially: this is known as a compound return.

## A long-term dynamic

The effect of compounding may seem negligible in the early years, but it could become very significant over the long term, as shown by this diagram:

In the context of a systematic savings strategy, this dynamic could become even more attractive. Suppose, for example, that you have \$175,000 invested in your RRSP, and that you make an additional contribution of \$12,000 each year. With a compound annual return of 5%, you would have about \$861,000 after 20 years, and more than half of that amount would consist of gains on your investment. Now suppose that you wait another 10 years: after 30 years, the same strategy would have produced gains of around \$1 million, and the total amount would be almost \$1.6 million. In those last 10 years alone, your strategy would have gained you twice as much as in the previous ten years.

## For illustrative purposes only

In “real life,” it is unlikely that anyone would obtain the same guaranteed compound rate year after year. In the context of a balanced portfolio, for instance, returns will vary from year to year depending on the performance of the assets held in the portfolio, and other calculation tools could be more appropriate.

Even though it is mainly useful for illustrative purposes, the theory of compound returns can nonetheless serve to illustrate the importance of three major principles within a savings strategy:

• reinvest profits (usually allowed by mutual funds);
• invest new money systematically every year or, better still, every month;
• and in the case of an RRSP, reinvest the tax savings generated by contributions, if possible.

If you would like to explore scenarios based on your own assumptions, there are various online calculators, including a very well designed one on the Ontario Securities Commission’s Get Smarter About Money website.

* This assumption is used for illustrative purposes only, to facilitate calculation and comprehension. It does not constitute an expectation of an actual return.

Get Smarter About Money, “Compound Interest Calculator.”
Investopedia, Compound interest.”
Lumen Finite Math, “Compound Interest and Exponential Growth.”