# Compound interest makes money sense!

It is a concept that is quite straightforward, but one that makes such a difference to the idea of putting a little something away for a rainy day. With compound interest, even making small but regular savings can transform a modest piggy bank amount into a respectable nest egg.

Compounding, simply put, means that any interest earned on an initial investment is deposited into the same account, and the resulting larger total then earns more interest – that is, earning interest on interest, as well as on the base capital. From then on, the interest that was added also itself earns interest. The next lot of interest is then added to the pile, and interest is consequently calculated on that now larger amount – and so on. So your savings continue to grow because your money earns more money.

It is a process that is helped greatly by adding regular amounts to the deposit. The power of compound interest combined with these regular savings can probably be best illustrated with an example.

Say a 16 year old school kid gets a part-time job at the supermarket, and takes his mum’s advice to save a little bit each week. If he saves just \$20 a week and puts this into a cash savings account at 5% interest, at the end of five years he will have accumulated \$5,917. This is made up of the initial \$20, then 52 weeks of \$20 deposits (\$1,040) done five times (for the five years; so \$5,200), and interest of \$697 (which for this exercise is calculated and compounded each week – in line with the regular deposits).

After five years, now aged 21, our young saver ups his weekly deposit to \$50. So from then until five more years, the total in his savings account will amount to \$22,282. And if he could arrange to make the weekly amount \$100, it would be \$37,011.

However the interest rate is stuck on 5% for these calculations, when in reality we all know that rates rise and fall.

Say then (just for fun, and rates seem to be heading north anyway), the interest rate rises to 8% by the time our 16 year old turns 21. So with 5% for five years saving \$20 a week, then 8% for another five years of \$100 a week, our 16 year old compound saver will turn 26 with \$46,346 tucked away. Quite a handy amount to have at that age (or any age), and he’d be in a much better financial position than his mates who didn’t take their mums’ advice on compounded savings.

If you want to make you own calculations, the Australian Securities and Investments Commission’s consumer website Fido has a compound interest calculator which can help. But here’s a quick back-of-envelope method of working out how long it will take to double your money from a compound interest investment.

The Rule of 72

Called the ‘Rule of 72’, this is a simplified way to work out how long an investment will take to double, given a fixed annual rate of interest. It is one of those ‘rule-of-thumb’ principles, but can help you gauge an investment’s worth before committing.

Simply, you divide the number 72 by the annual rate of return to get the number of years it will take to double the value of your original investment. So for a rate of 10% a year, 72 divided by 10 equals 7.2 (so just a little over seven years to double your money). A rate of 5% will require 14.4 years, 3% will keep you waiting 24 years, and so on.

The Rule of 72 is not absolutely precise, but will give you a practical estimate. Even ASIC has suggested that rules-of-thumb such as these can be useful indicators, should investors have one of those ‘too-good-to-be-true’ inklings about potential investments. (See ASIC’s warning here, and its suggested use of the Rule of 72.)

History buffs may find it interesting to note that the Rule of 72 has been circulating for centuries. It was published in 1494 by Italian mathematician Luca Pacioli, a collaborator of Leonardo da Vinci, but was probably known and used long before then.

And as a rule-of-thumb it can be surprisingly accurate – especially for one that is at least 500 years old. The rule is accurate to within six months as long as the interest rate is at least 4%, as shown in this Rule of 72 spreadsheet provided by Dr John Banks from the Department of Mathematics and Statistics at La Trobe University in Melbourne.