The Modern-Day Miracle of Compound Interest

'Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it.'

This article was first sent to Fools as an email in our 'The Good, The Bad and The Ugly' series.

The above quote is often attributed to Albert Einstein, a man famous for discovering several of the universe's secrets. It's also claimed that Einstein described compound interest as `the eighth wonder of the world', but this quote has been credited to Benjamin Franklin and John Maynard Keynes, among others.

Then again, you don't need to be a genius to understand the power of compound interest. Indeed, I learnt the above lesson the hard way, during a borrowing binge that lasted most of the Nineties and left me almost £50,000 in debt! Nowadays, instead of paying interest, I earn it, so compound interest has become my friend, not my enemy.

Let me show you what I mean, using three simple examples:

1. A savings account paying 6% a year

Let's say that you have £1,000 in a tax-free savings account (such as a cash ISA) which pays yearly interest of 6%. If you leave this interest to roll-up in your account, then here's what happens:

After one year, your £1,000 earns interest of £60 and your balance is now £1,060. The following year, this balance earns interest of £63.60 (the original £60 of interest, plus a further £3.60 of interest on the original £60 of interest). In year three, your interest is £67.42 and your balance rises to £1,191.02. This virtuous circle continues until, after ten years, you have £1,790.85 -- your original grand, plus almost £800 in interest. Not bad, agreed?

Now let's look at the flipside of the coin: paying compound interest:

2. An overdraft charging 1% a month

Let's say that you have an overdraft of £1,000, on which your bank charges interest at 1% a month (12.68% APR). After one month, you owe £1,010 -- your debt, plus £10 of interest. The next month, you are £1,020.10 in the red. This continues until, at the end of the year, you owe £1,126.83. In other words, in twelve months, your overdraft has increased by more than an eighth, or 12.68%. Oops!

Now let's look at an even more unpleasant example of compound interest working against you:

3. A credit card charging 2% a month

Let's say that you owe £1,000 on a credit card which charges 2% a month (26.82% APR). Assuming that your monthly repayments are exactly balanced by equal spending, then your debt will build and build. After one month, you owe £1,020 and, after two months, £1,040.40. This vicious circle continues until, by the end of the year, you owe £1,268.24 and your debt has increased by more than a quarter (26.82%). Ouch!

So, the next time you're tempted to buy that `must-have item' by dipping even deeper into your credit limit, please stop and think. When you combine high rates of interest on debt with the impressive power of compound interest, you become a big loser. Indeed, that extra £500 on your credit card could cost you £1,000 in interest before you pay it off!