Compound Interest

Today in class we learned about compound interest..

Compound Interest


is the concept of adding accumulated interest back to the principal, so that interest is earned on interest from that moment on. The act of declaring interest to be principal is called compounding (i.e. interest is compounded).

Compound Interest

is great when you are investing because the interest your investments earn is also earning interest. Compound interest is not so great when you borrow money because it costs more than simple interest. The longer your investment is compounding, the greater the amount of interest you earn. If you invest for a long term, it is in the last years of the term that you see the biggest impact of compounding. The earlier you start saving, the more time there is for an investment to grow. Interest is not always compounded annually. Some financial institututions add interest to the principal every six months. In that case, the interest is compounded semi-anually. There are also daily savings accounts, where interest is compounded on a daily basis.



Terms of compound interest

-Compounded annually

-Compounded daily

-Compounded semi-anually

The rule of 72

To quickly estimate the length of time it takes for an investment to double, use the rule of 72. All you need is the interest rate and the number 72. Divide 72 by the interest rate(as a number, not a percentage) to find the time in years. If the interest rate is 10%, divide 72 by 10 to find the time in years: 72/10=7.2 years. Note that 7.2 years is not 7 years and 2 months. It is 7 years plus 0.2 times 12 months. 7.2 years is therefore 7 years plus 2.4 months.



The 'Rule of 72' is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself. For example, the rule of 72 states that $1 invested at 10% would take 7.2 years ((72/10) = 7.2) to turn into $2. In reality, a 10% investment will take 7.3 years to double ((1.10^7.3 = 2).When dealing with low rates of return, the Rule of 72 is fairly accurate. This chart compares the numbers given by the rule of 72 and the actual number of years it takes an investment to double.




Rate of Return
Rule of 72
Actual # of Years
Difference (#) of Years
2%
36.0
35
1.0
3%
24.0
23.45
0.6
5%
14.4
14.21
0.2
7%
10.3
10.24
0.0
9%
8.0
8.04
0.0
12%
6.0
6.12
0.1
25%
2.9
3.11
0.2
50%
1.4
1.71
0.3
72%
1.0
1.28
0.3
100%
0.7
1
0.3Notice that, although it gives a quick rough estimate, the rule of 72 gets less precise as rates of return become higher. Therefore, when dealing with higher rates, it's best to calculate the precise number of years algebraically by means of the future value formula.