# Compound interest and the rule of 72

With that in mind, would you rather have R1,000 a day for 30 days or R1 whose value has doubled every day for 30 days? Connoisseurs would choose the doubling of R1. Why? Because after 30 days they would have accumulated over R500 million – compared to the R30,000 they would have had they opted for R1,000 a day.

**What is the difference between compound interest and simple interest?**

In short, with simple interest you only earn interest on the original amount you invested, whereas compound interest is “interest earned on interest” and it is calculated on the principal amount as well as the interest from the previous period.

Auto loans and consumer loans use simple interest while estimating interest payments. Even cash deposits use simple interest to calculate investment return. Borrowers benefit more from simple interest because there is no compounding power. In other words, there is no interest on interest.

Compound interest has the potential to generate more returns than simple interest. An investment grows exponentially with compound interest because it is based on the principal power of compounding. Compound interest is most often used in investments where there is reinvestment of profits.

**How does compound interest work?**

The principle is simple: one rand invested at an annual return of 10% will be worth 1.10 rand in one year. Invest that R1.10 and get 10% again, and you’ll end up with R1.21 two years from the day of your initial investment. The first year only brought you R0.10, but the second year generated R0.11. And this is the basic principle of compound interest – earnings on earnings. Increase the time and amount invested and the gains become more and more pronounced.

In the words of Albert Einstein: “Compound interest is the eighth wonder of the world. Whoever understands it, wins it. Whoever doesn’t, pays.

**The Rule of 72**

A great tool to have in your toolbox when looking at your investments earning compound interest is the “Rule of 72”. The Rule of 72 is a mathematical principle that estimates how long it will take for an investment to double in value and is a basic formula anyone can use.

Simply take the number 72 and divide it by the interest earned on your investments each year to get the number of years it will take for your investments to grow by 100% or double.

Below is a graphical illustration of the ruler. For example, if an investment earns 10% per year, its value will double in about seven years. Conversely, for an investment to double in seven years, it must generate an annual rate of return of 10%.

Let’s say you invested R10,000 at an annual rate of return of 9.1%, which is the annualized return of the Morningstar Balanced Portfolio over the past seven years. To calculate the doubling time using the rule of 72, you need to enter the numbers into the formula as follows:

72 ÷ 9.1 = 7.9 years

This means that your initial investment of R10,000 will be worth R20,000 in about 7.9 years, assuming your earnings accumulate. All of this also assumes that you don’t make additional contributions to your investment over time, which makes it even more impressive that your money has doubled in less than a decade.

**The earlier you start, the more likely you are to reach your goal**

Let’s take a simple example of two investors who both aspire to become millionaires.

**Investor A**

Investor A is sensible and manages to save his rands and, from 24 to 30 years old, manages to invest 2,000 rands per year in a portfolio recommended by his financial adviser.

His investment increases each year by 12% (net), and although he stopped saving after he turned 30, he left the money invested where he continued to earn 12% each year until his retirement at age 65.

**Investor B**

Investor B, on the other hand, continued to spend his money for another six years before starting to save R2,000 per year at age 30, also earning 12% (net) per year through the same advisor. However, Investor B was able to continue investing R2000 per year until he retired at the same time as Investor A, i.e. at the age of 65.

So, did any of them achieve their goal of making a million? In the end, the two were pretty much successful.

**The difference is **that because sensible Investor A started early, he only had to invest R12,000 (i.e. R2,000 for six years), while Investor B needed to invest R72,000 (R2,000 for 36 years) (or six times the amount that Investor A invested) to arrive at the same point. Therefore, this six-year delay effectively cost Investor B R60,000.

**A lesson to remember**

Whether our financial goal is to become a millionaire, retire comfortably, or become financially independent, the benefit of compound interest is that it helps us achieve those goals.

Investing as early as possible can be as important as the actual amount invested over a lifetime. Therefore, to truly reap the magic of compounding, it’s important to start investing – or paying down debt as the same principle applies in reverse – as early as possible. Always remember that due to the effect of compound interest or compound returns, gains lead to gains, which lead to even greater gains. This is the real power of compound interest.

*Roné Swanepoel, Head of Business Development at Morningstar Investment Management SA*

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