The Rule of 72

There are a number of basic rules that one should be aware of with regard to investing and growing wealth. One of these rules is the "Rule of 72".

The Rule of 72 basically states that any two numbers that can multiply to equal 72 will tell you how long it will take to double your investment assuming compounding.

Simply put: R x T = 72

Where:

R = Rate of Return

T = Time

Look at the following examples:

• 7.2 x 10 = 72 If you invest $10,000 and get a compounded return of 7.2%pa, you would double your investment to $20,000 in 10 years

• 14.4 x 5 = 72 If you invest $10,000 and get a compounded return of 14.4%pa, you would double your investment to $20,000 in 5 years

• 20 x 3.6 = 72 If you invest $10,000 and get a compounded return of 20%pa, you would double your investment to $20,000 in 3.6 years

Other ways to look at the formula are as follows:

R = 72/T

or

T = 72/R

Applying these to practical situations:

Q. If you invest $100,000 at an annual Rate of Return of 6.7%pa, how long will it take to double your investment to $200,000?

A. T=72/R T=72/6.7 T=10.75 years

Q. What annual Rate of Return do I need in order to double my investment from $100,000 to $200,000 in 4 years?

A. R=72/T R=72/4 R=18%pa

Q. Current bank savings interest rates are at 1% pa. If I invest $100,000, how long would it take to double my money?

A. T=72/R T=72/1 T=72 years

These simple rules do not take taxation into account. They assume simple compounding where none of the money (neither principal or interest) are touched for the set period.

As such, the Rule of 72 is a guide for quick calculations and allows one to quickly work out rates of return.

However, there is one more area that it can be used for..... In my previous post, I stated that cash held in a bank, under your mattress, in a tin buried in your back yard, will lose value each year due to inflation. As such, the rule of 72 can apply to this situation also.

For example:

Q. If you have $100,000 in your home safe, and the rate of inflation is 4.5% pa, how long will it take for your $100,000 to halve in value?

A. T=72/R T=72/4.5 T= 16 years

Here is a real practical application question for you to apply your new knowledge to:

Q. You have purchased a new house. It's market value at time of purchase was $870,000. Houses in the area are appreciating at a consistent rate of 8% per year. How long will it take for your house to double in value and become $1,740,000?

A. T=72/R T=72/8 T=9 years

The last example shows how in just 9 years, a property will double in value, if the rate of capital growth is 8%.

In Sydney Australia, property prices double roughly every 9 years. As such, we can calculate that, on average, properties increase in value by roughly 8% pa compounded annually.

Now imagine that you purchased a $500,000 property back in 2002 and had a $450,000 mortgage (90% LVR). If you still has that property today, by using time, inflation, the Rule of 72, and by not selling the investment and as such creating no actual taxable events, the property would be worth about $2,000,000 today in 2022.

Even if you had not paid a single cent of the principle back, you can see how the LVR has decreased to 22.5% just because of inflation. You would have turned your $50,000 deposit back in 2002 into $1,550,000 in 2022.

Remember in a previous post, I stated that in late 1987 my wife and I purchased our first house. If we apply what I said above about how property prices double about every

9 years here in Sydney, then:

1987 $97,000

1996 $200,000

2005 $400,000

2014 $800,000

2022 $1,500,000

Now THAT is how inflation and time can be used to your advantage!

And since the property was not sold, there was no taxable event for the 35 years that it was held - so maximum compounding!