When you invest in savings instruments, you earn interest at a contractual interest rate. The interest rate is usually stated as a yearly rate. For example, if you invest $1,000 in a certificate of deposit (CD) that pays an annual interest rate of 6%, a year later you will have $1,060. The $60 in interest you earn in a year is your compensation for deferring consumption today.
If you decide to invest the $1,060 for another year at 6%, a year later you will have $1,123.60. In the second year, you earn $63.60 in interest, or $3.60 more than in the first year. This is because your investment is, in part, "earning interest on interest." This example illustrates a fundamental principle of saving and investing called compounding.
The following table shows the benefit of compounding on a $1,000 lump-sum investment. The investment is made for a range of interest rates and investment periods. For example, the table shows that $1,000 invested for three years at 8% grows to $1,260. These values are called future values. Future values are rounded to the nearest dollar. The values based on annual (once a year) compounding. We'll soon see the importance of compounding frequency on the future value of an investment:
Years 4.0% 6.0% 8.0% 10.0%
1 $1,040 $1,060 $1,080 $1,100
3 $1,125 $1,191 $1,260 $1,331
5 $1,217 $1,338 $1,469 $1,611
10 $1,480 $1,791 $2,159 $2,594

Looking at the table, we see that $1,000 invested for 10 years at 8% has a future value of $2,159. Average interest earned each year on this investment is $115.90 [($2,159-$1,000)/10]. If the same investment were made for five years, average yearly interest declines to $93.80 [($1,469-$1,000)/5]. For three years, average yearly interest declines further to $86.70 [($1,260-$1,000)/3]. Higher average interest earnings for longer investment periods reflect the benefit of compounding.
For example, enter $1,000, 6%, and 5 years in the first, second, and fourth boxes. Be sure that the round button labeled "Yearly" is selected. Enter a zero in the other boxes. View Results by clicking the tab, which show $1,338. This is the same value in the table above. Interpretation: the future value of $1,000, invested for five years at 6% interest, is $1,338. (Note: By entering zeros elsewhere, we ignore taxes, interest, and assume we make no additional investments.)
Generally, the more frequently you compound your investment, the greater the future value. While the table above shows future values for investments that are compounded annually, financial institutions routinely compound your investments on a quarterly or monthly basis. Some financial institutions even offer continuous compounding.
The following table reproduces the future values in the table above. Only this time, the $1,000 investment earns interest that is compounded on a quarterly basis (four times a year):
Years 4.0% 6.0% 8.0% 10.0%
1 $1,041 $1,061 $1,082 $1,104
3 $1,127 $1,196 $1,268 $1,345
5 $1,220 $1,347 $1,486 $1,639
10 $1,489 $1,814 $2,208 $2,685

As you can see, the increase in compounding frequency increases the future values. Most dramatic increases occur at the highest interest rate and for the longest periods. For example, from the top table, $1,000 that is compounded annually at 10% for 10 years is worth $2,594. Compounded quarterly, the same investment grows to $2,685. This is an extra $91 of interest you earn as a result of more frequent compounding. If the same investment is compounded daily, it grows to $2,720. This is an extra $126 in interest over yearly compounding. Clearly, an increase in compounding frequency benefits the growth of your investment.
More than likely, you will want to make additional contributions to your original investment. Regular contributions to your investment fuel its growth, producing a much larger future value. Let's look at an example.
The following table is a reproduction of the table, at top. In this case, the table shows future values for the original $1,000 investment, together with monthly contributions of $100. (Contributions are assumed to be made at the beginning of every period):
Years 4.0% 6.0% 8.0% 10.0%
1 $2,267 $2,301 $2,336 $2,372
3 $4,958 $5,150 $5,351 $5,561
5 $7,873 $8,361 $8,887 $9,454
10 $16,265 $18,289 $20,636 $23,362

Future values begin to take off as a result of your making regular monthly contributions. For example, an initial investment of $1,000 and monthly contributions of $100, invested at 8% for five years, grows to $8,887. From the top table, we saw that a lump sum investment of $1,000 grows to a future value of $1,469. The difference in returns ($8,887-$1,469), or $7,418, represents the monthly contributions and the interest earned on the monthly contributions over the five years. Since these contributions add up to $6,000 ($100*60), the $1,418 ($7,418-$6,000) is the total interest earned on the contributions.
We've seen how compounding can boost the value of your investment. In general, the greater the frequency of compounding, the greater the future value of your savings. It pays to ask financial institutions to explain the rate of compounding that they use to either pay you interest on a deposit or charge you interest on a loan.
We've also seen how making additional deposits adds discipline to your savings program and results in a much greater future value. It's important that you are saving more than you withdraw each period. If you take out more than you save, you will lose a great deal of the compounding benefits.
The above information is educational and should not be interpreted as financial advice. For advice that is specific to your circumstances, you should consult a financial or tax adviser.
2008-07-21 15:28:18

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