Compound interest: A building block of wealth

Bina Brown
For CNN

Adjust font size:

(CNN) -- Legend has it Albert Einstein called compound interest the greatest mathematical discovery of all time -- or something to that effect.

With official interest rates on the rise in most countries possibly resulting in higher debt repayments for many people, it is worth revisiting this phenomenon.

Compound interest is one of the basic building blocks for saving up money, investing, and building a nest egg.

If you owe money and are paying interest then you are also likely to be paying compound interest on the loan, which means that the slower you pay it off, the more you have to pay.

Roughly, a 0.25 percent rise in official interest rates will add $5 a week interest for every $100,000 owed.

Financial planning veteran Noel Whittaker explains that the repayments are normally shown as factors, which depend on the interest rate and the term of the loan.

A loan of $100,000 at 7 percent and paid it back at $899 a month would mean the loan would be paid off in 15 years.

While a relatively small increase in repayments can reduce a loan from 30 years to 25 years, it takes a big increase in repayments to increase it from 10 years to five years.

A loan of $100,000 at 7 percent being paid back over 30 years would mean monthly repayments of $665 a month, making total interest payable would be $139,400.

Whittaker says that by increasing those payments by just $42 a month to $707 a month would drop the term to 25 years and interest paid would be $112,100.

Also important is the how the effect of the rate diminishes as the loan term reduces. A $100,000 loan at 7% over 30 years requires $665 a month. If the rate goes to 9 per cent payments increase to $805 a month -- an overall increase of $273 a month.

However, if the term was 10 years, an increase in rates from 6.5 per cent to 9 per cent could cause repayments to increase from $1,135 a month to $1,267, an overall increase of just $132 a month.

"This is why I urge people to pay their loans back at $12 a $1,000 a month if possible. That will reduce the term to approximately 10 years and take interest rates out of the equation as the term of the loan will be largely unaffected by rate fluctuations," says Whittaker.

On the flip side, saving $10 a week might not sound like much but putting the $510 a year into an investment vehicle paying 6 per cent compound interest for ten years would give you about $7,000.

Increase the length of time it is invested and the rate of return and the amount to be saved could be considerable.

Crunching the numbers at IPAC Securities, Colin Lewis says that the $510 invested in an account yielding simple interest at 5 percent would give an extra $25.50 at year end. After year one you will have $535.50; after year two, $562; after year three, $590; and so on.

The same amount of money put in an account that returns 5 percent compound interest will not only mean interest is earned on the original $510 but on the interest that is added to it.

At the end of year one there will be $535.50. In year two it will be 5 percent of $535.50, not of $510. So instead of getting $25.50 added to the money it will be $26.78, bringing a total of $562.28. The next year $28.11 is added. Then $29.51 the year after.

This difference between compound interest and simple interest might not seem much but it increases considerably with two factors: time and rate of return.

If the interest comparison is expanded out 25 years. The simple-interest will grow 25 times $25.50 to $637.50 giving a total balance of $1,147.50. The compound interest nets $1,727.04 or $1217.04 interest.

If the same $510 earns 10 percent rather than 5 percent the money will grow to $5,525.70. Invest it for another other 10 years and your money grows to $14,332.24.

Because the total amount of your money grows each year, the amount that is added on each year grows right along with it. The impact of putting in the $510 a year every year would yield an even greater result.

Whether Einstein actually called it the eighth wonder of the world or the most powerful force in the universe, it is a mathematical discovery everyone should try to understand.

Get up-to-the minute news from CNN CNN.com gives you the latest stories and video from the around the world, with in-depth coverage of U.S. news, politics, entertainment, health, crime, tech and more.

---

• Mom dies, gives birth, then is revived
• Who is Michael Adebolajo?
• Gas explosion kills 17 children in minivan
• Experts: 'Minor errors' in stem cell study
• School district, student at odds over tweet

• Irish PM to quit over payments scandal
• NATO chief: Afghan troop increase likely
• Militants hunted as calm retuns to Basra
• Pressure on Bush to skip Olympics
• BA sending misplaced T5 baggage to Milan

• Recruiting suicide bombers (2:50)
• London was lucky (2:36)
• Cars in London rigged as bombs (3:48)
• Second explosives-packed car foun (2:32)
• Soviet culture returns (3:47)