# Compound Interest an Investor's Friend

Popular phrases, such as "time is money" and "a penny saved is a penny earned," allude to the interrelationship of time and money. Even small amounts of savings, combined with a decades of compound interest, can grow to significant sums. Compound interest, very simply, is the calculation of interest on reinvested interest, as well as on the original amount invested.

It is reported that Albert Einstein once called compound interest "the most powerful force in the universe." It has also been referred to as "the eighth wonder of the world". Compound interest on well-chosen investments over time has been shown to be a primary factor in wealth accumulation by millionaires.

A dollar that is saved or invested wisely will be worth more in the future than it is today. Future value is the amount that a sum of money will be worth at a later date when it is compounded for a certain time period at a certain interest rate. The longer the compounding period, and the higher the interest rate, the larger its future value.

For example, a one-time \$2,000 deposit would be worth \$16,299, \$54,733, and \$814,774 at age 65 and \$20,803, \$80,421, and \$1.64 million at age 70, at 5%, 10%, and 15% rates of return, respectively, according to the book Getting Rich in America. Over long periods of time, differences between the total accumulation at various investment returns are substantial.

The Rule of 72 provides is a simple way to illustrate the impact of compound interest. To estimate how long it will take to double a sum of money (any amount), at a given rate of return, divide 72 by the interest rate. The result is roughly the number of years before an initial sum will double. Money will double in seven years at 10%, eight years at 9%, nine years at 8%, ten years at 7%, and 12 years at 6%.

The Rule of 72 can also be used in reverse to calculate the interest rate required to double money. Simply divide 72 by the specified time period. For example, 72 divided by 8 years = 9% interest. To double your money in five years requires almost a 15% average annual return. The Rule of 72 assumes that the interest rate stays the same for the life of an investment and that all earnings are reinvested.

The higher an investor's return, the faster it takes money to double because there will be more "doubling periods" within a specific time frame. The trade-off, of course, is the higher risk associated with investments that have historically provided a higher rate of return, as investors have experienced recently.

To illustrate the relationship between the Rule of 72 and compound interest, consider two investors who are both age 42 and receive a \$50,000 lump sum pension distribution. Investor A averages a 6% return and has two 12-year doubling periods (72 divided by 6 = 12) through age 66 while Investor B averages a 9% return and has three 8-year doubling periods (72 divided by 9 = 8). At the end of 24 years, Investor B has twice as much money (\$400,000) as Investor A (\$200,000).

Like the progression of prizes on the popular game show Who Wants To Be a Millionaire?, the final rounds of doubling are the most profitable because you are doubling larger amounts. It would only take Investor B another eight years (age 74) to double \$400,000 to \$800,000 and eight more years (age 82) to accumulate \$1.6 million. Meanwhile, Investor A would have a comparatively low \$400,000 at age 78.