# Compounding interest

#### stanbusk

Staff member
Compounding interest is the Interest added to interest previously earned on a principal balance. It is the process of reinvesting each interest payment to earn more interest. Compounding is based on the idea that interest itself becomes principal and therefore also earns interest in subsequent periods.

The more frequently interest is compounded, the higher the effective yield. Loan calc allows you to select from the most used compoundings:

- Continuous Interest compounded every day = 365 x year
- Weekly Interest compounded every week = 52 x year
- Biweekly Interest compounded every two weeks = 26 x year
- Monthly Interest compounded each month = 12 x year
- Quarterly Interest compounded each quarter = 4 x year
- Semiannually Interest compounded twice per year = 2 x year
- Annually Interest compounded once per year = 1 x year

and also less used:

- Half-month Interest compounded once per year = 24 x year
- 4 weeks Interest compounded once per year = 13 x year
- 2 months Interest compounded once per year = 6 x year
- 4 months Interest compounded once per year = 3 x year

It is amazing that something as important as interest rates are so generally misunderstood or regarded so lightly. The effect of these rates on purchases and investments can often make the difference between financial success or failure. Then consider the compounding of interest, and the effect of time and the importance of understanding this is increased. Buy a house, use a credit card, invest in a stock, bond, or mutual fund, the effect of compounding can change your approach to all areas of finance. Making some simple comparison to prove the point, it is easy to demonstrate the importance of considering compounding in all types of financial transactions.

One way to see the importance of compounding of interest is to look at what happens when interest is compounded. If you see a bank advertise that an interest rate is compounded they will usually show the stated rate and the effective rate. For instance a rate of 5% apr compounded has an effective rate of approximately 5.125% apr. While .125% doesn't sound like much what it means is an extra \$1.25 per thousand dollars each year. For \$100,000 put in a bank for 10 years this would amount to an additional \$1250! The interesting part is that as the base interest rate increases the difference between it an the effective rate when compounded gets larger. For example above at 7% apr with compounding the additonal yeild above the base interest would amount to about \$1900 over the same ten year period.

Time also has an effect that is also important. Take the same figure \$100,000 and pay off a mortgage loan at 7%. If you choose to pay over 20 years your monthly payments would be \$775.30, you would pay a total of \$186,072.00 of which \$86,072 would be interest. If you chose a 25 year mortgage at the same 7% rate your monthly payments would be \$706.78 and you would pay a total of \$112,034.00 in interest. If you decided on a 30 year mortgage with the same 7% rate, your monthly payments would be \$665.30 and you would pay \$139,508.00 in interest. The additional 10 years of mortgage payments, while saving you \$41.48 in payments each month, would cost you an additional \$53,436 in interest payments over the 10 year difference in terms of the loan!

Then of course there is the difference of a few fractions of percent on the rate on a loan or return on investment. Most people will not spend the time to shop around to save one percent, much less 1/4%. The often will express the feeling that it really doesn't make that much difference. Well take a look at the difference between the \$100,000 30 year mortgage at 7% and the same one at 7.25%. While the interest rate is only one quarter of one percent different the difference in interest paid over the 30 years is \$33,550 or over \$1,000 per year! For investments the difference in return can be figured using a tool called the rule of 72.

The rule of 72 is that given a rate of return in percentage, you can take that number and divide it into 72 and calculate how long it will take you to double your money. For example a 9% return will double every 8 years. I often hear people say things like, "8 percent or 9 percent it's really not that big a difference." Well look at two investments of \$1000 invested for 2 children's trust to be turned over at age 32 at each of these percentages. Let's say both were started in 1970. In 1978, 1986, 1994, and 2002 the 9% investment would double so in 2002 its value would be \$16,000. The investment fund at 8% would double in 1979, 1988, 1997, and 2006.

It's value would be only approximately \$11,200 in 2002, with four years before it would reach \$16,000!

Interest and return rates are key to all financial considerations. To pass off even the slightest difference as unimportant can be a mistake. In any financial transaction it is important to know your rates.

Written by Charles Grimmett - Â© 2002 Pagewis
The power of the compounding interest formula