“The most powerful force in the universe is compound interest”
-Albert Einstein
Einstein was obviously inspired by the amazing ability of money to build through compounding interest. But what is compounding interest? How is it calculated? We often hear the term thrown around by banks and investors. We read it in books and occasionally hear something on the television or radio about it. So what is it? Compounding interest is a concept of adding accumulated interest back to principle. This results in interest being earned on the interest from the moment it is added back in. Compounding interests effect is largely dependent on the frequency with wish interest is compounded and the rate which is applied.
With a small definition of what compound interest is out of the way, let’s move on to the calculations. To do so, we will need to be familiar with a few terms:
P is the initial amount (either what you borrow or what you put in)
r is the annual rate of interest
n is the number of years the amount will be in place
A is the amount of money accumulated over n years, to include interest.
The formula then is as follows:
A = P(1+r)n
For example:
The amount accumulated if you deposited $1,000.00 into a cd with a 12 month interest rate of 4.5% is:
A = 1000(1+.045)1
A = 1045
However, if you let that CD stretch out for 5 years.
A = 1000(1+.045)5
A = 5225
This formula can also be modified if the frequency of interest calculations is not done on an annual basis. For example some interest is compounded Monthly, or Quaterly. In this case you would modify the formula to reflect the interval.
Example:
Quaterly Interest would be calculated as:
A=P(1+4/4)^4
Banks such as mine usually calculate interest over a period of 12 months. Their calculations look like:
Monthly:
A = P(1+r/12)^12
One final calculation that is worth mentioning is the “Rule of 72”. The Rule of 72 is a simple way to demonstrate the growth potential of compound interest. Essentially the rule says:
72/ i = N
i is the interest rate and n is the number of time periods it would require to double your money.
For example, say a mutual fund grows at 9% average interest rate per year. According to the rule of 72, if money were invested in this mutual fund, then it would double every 8 years.
72/9 = 8
Compound interest is an excellent mathematical tool for getting rich but remember banks use it to get rich also! Car loans, credit cards, mortgage payments are all subject to compounding interest. The longer you stretch the loan terms the higher your bottom line cost is going to be. Same logic applies for investments also! The longer you stay in, the higher your return*. I hope this article has shed some light on the subject of compound interest and that you found it useful. Also see the full Wikipedia article about compound interest which has much more in depth mathematics involving compound interest.
If you would like to make a comment, please fill out the form below.
[...] a savings account, a money market account or CD. This is so that you can benefit from the power of compounding interest while you save and will be less tempted to spend it unnecessarily. Set up an auto-savings plan if [...]