With compound interest, it is calculated not only at the beginning, but on any money accumulated in the meantime. It is calculated each period on the original principal and all monies accumulated during past periods.
Albert Einstein called compound interest “the greatest mathematical discovery of all time”. We think this is true partly because, unlike the trigonometry or calculus you studied back in high school, compounding can be applied to everyday life.
The wonder of compounding (sometimes called “compound interest”) transforms your working money into a state-of-the-art, highly powerful income-generating tool. Compounding is the process of generating earnings on an asset’s reinvested earnings. To work, it requires two things: the re-investment of earnings and time. The more time you give your investments, the more you are able to accelerate the income potential of your original investment, which takes the pressure off of you.
To demonstrate, let’s look at an example:
If you invest $10,000 today at 6%, you will have $10,600 in one year ($10,000 x 1.06). Now let’s say that rather than withdraw the $600 gained from interest, you keep it in there for another year. If you continue to earn the same rate of 6%, your investment will grow to $11,236.00 ($10,600 x 1.06) by the end of the second year.
Because you reinvested that $600, it works together with the original investment, earning you $636, which is $36 more than the previous year. This little bit extra may seem like peanuts now, but let’s not forget that you didn’t have to lift a finger to earn that $36. More importantly, this $36 also has the capacity to earn interest. After the next year, your investment will be worth $11,910.16 ($11,236 x 1.06). This time you earned $674.16, which is $74.16 more interest than the first year. This increase in the amount made each year is compounding in action: interest earning interest on interest and so on. This will continue as long as you keep reinvesting and earning interest.
Consider two individuals, we’ll name them Pam and Sam. Both Pam and Sam are the same age. When Pam was 25 she invested $15,000 at an interest rate of 5.5%. For simplicity, let’s assume the interest rate was compounded annually. By the time Pam reaches 50, she will have $57,200.89 ($15,000 x [1.055^25]) in her bank account.
Pam’s friend, Sam, did not start investing until he reached age 35. At that time, he invested $15,000 at the same interest rate of 5.5% compounded annually. By the time Sam reaches age 50, he will have $33,487.15 ($15,000 x [1.055^15]) in his bank account.
What happened? Both Pam and Sam are 50 years old, but Pam has $23,713.74 ($57,200.89 – $33,487.15) more in her savings account than Sam, even though he invested the same amount of money! By giving her investment more time to grow, Pam earned a total of $42,200.89 in interest and Sam earned only $18,487.15.
Editor’s Note: For now, we will have to ask you to trust that these calculations are correct. In this tutorial we concentrate on the results of compounding rather than the mathematics behind it. (If you’d like to learn more about how the numbers work, see Understanding The Time Value Of Money.)
Both Pam and Sam’s earnings rates are demonstrated in the following chart:
You can see that both investments start to grow slowly and then accelerate, as reflected in the increase in the curves’ steepness. Pam’s line becomes steeper as she nears her 50s not simply because she has accumulated more interest, but because this accumulated interest is itself accruing more interest.